Complete Classical Eight-Row Connective Tables
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This question bank has corresponding bilingual step-by-step derivations. Source candidate and English ai_candidate states are retained. AI review, finite computation and Lean formal proof are labelled separately.
batch-20261009-advance-20261013-r05-logical-connectives-foundations · 2026-10-09 · 100 questions
This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.
1. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 0, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
2. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 1, 1, 1, 1, 1, 1, 1]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([True, True, True, True, True, True, True, True], [True, True, True, True, True, True, True, True])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [True, True, True, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
3. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 0, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([False, False, False, False, False, False, False, False], [True, False, False, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [True, False, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
4. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 0, 0, 0, 0, 0, 0], B=[1, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([True, False, False, False, False, False, False, False], [True, False, False, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, False, False, False, False, False, False], [True, False, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
5. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 0, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([False, False, False, False, False, False, False, False], [False, True, False, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [False, True, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
6. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 0, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([False, False, False, False, False, False, False, False], [True, True, False, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [True, True, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
7. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 0, 0, 0, 0, 0, 0], B=[1, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([True, False, False, False, False, False, False, False], [True, True, False, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, False, False, False, False, False, False], [True, True, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
8. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 0, 0, 0, 0, 0, 0], B=[0, 1, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([False, True, False, False, False, False, False, False], [False, True, False, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, False, False, False, False, False], [False, True, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
9. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 0, 0, 0, 0, 0, 0], B=[0, 1, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([False, True, False, False, False, False, False, False], [True, True, False, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, False, False, False, False, False], [True, True, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
10. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 0, 0, 0, 0, 0, 0], B=[1, 1, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([True, True, False, False, False, False, False, False], [True, True, False, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, False, False, False, False, False], [True, True, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
11. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 1, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([False, False, False, False, False, False, False, False], [False, False, True, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [False, False, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
12. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 1, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([False, False, False, False, False, False, False, False], [True, False, True, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [True, False, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
13. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 1, 0, 0, 0, 0, 0], B=[1, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([True, False, False, False, False, False, False, False], [True, False, True, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, False, False, False, False, False, False], [True, False, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
14. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 1, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([False, False, False, False, False, False, False, False], [False, True, True, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [False, True, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
15. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([False, False, False, False, False, False, False, False], [True, True, True, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [True, True, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
16. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[1, 0, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([True, False, False, False, False, False, False, False], [True, True, True, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, False, False, False, False, False, False], [True, True, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
17. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 1, 0, 0, 0, 0, 0], B=[0, 1, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([False, True, False, False, False, False, False, False], [False, True, True, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, False, False, False, False, False], [False, True, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
18. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[0, 1, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([False, True, False, False, False, False, False, False], [True, True, True, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, False, False, False, False, False], [True, True, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
19. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[1, 1, 0, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([True, True, False, False, False, False, False, False], [True, True, True, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, False, False, False, False, False], [True, True, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
20. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 1, 0, 0, 0, 0, 0], B=[0, 0, 1, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([False, False, True, False, False, False, False, False], [False, False, True, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, False, False, False, False, False], [False, False, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
21. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 1, 0, 0, 0, 0, 0], B=[0, 0, 1, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([False, False, True, False, False, False, False, False], [True, False, True, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, False, False, False, False, False], [True, False, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
22. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 1, 0, 0, 0, 0, 0], B=[1, 0, 1, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([True, False, True, False, False, False, False, False], [True, False, True, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, False, False, False, False, False], [True, False, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
23. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 1, 0, 0, 0, 0, 0], B=[0, 0, 1, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([False, False, True, False, False, False, False, False], [False, True, True, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, False, False, False, False, False], [False, True, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
24. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[0, 0, 1, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([False, False, True, False, False, False, False, False], [True, True, True, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, False, False, False, False, False], [True, True, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
25. Conjunction and Inclusive Disjunction Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[1, 0, 1, 0, 0, 0, 0, 0]. Give (A∧B truth table, inclusive A∨B truth table).
View answer and explanation
([True, False, True, False, False, False, False, False], [True, True, True, False, False, False, False, False])
Conjunction needs both True; inclusive disjunction needs at least one True. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, False, False, False, False, False], [True, True, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-and-or-table · candidate
26. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 0, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([True, True, True, True, True, True, True, True], [True, True, True, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [True, True, True, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
27. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
28. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 0, 0, 0, 0, 0, 1], B=[1, 0, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([True, True, True, True, True, True, True, True], [False, True, True, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [False, True, True, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
29. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 0, 0, 0, 0, 0, 1], B=[0, 0, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([False, True, True, True, True, True, True, True], [False, True, True, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, True, True, True, True, True, True], [False, True, True, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
30. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 0, 0, 0, 0, 0, 1], B=[0, 1, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([True, True, True, True, True, True, True, True], [True, False, True, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [True, False, True, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
31. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 0, 0, 0, 0, 0, 1], B=[1, 1, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([True, True, True, True, True, True, True, True], [False, False, True, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [False, False, True, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
32. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 0, 0, 0, 0, 0, 1], B=[0, 1, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([False, True, True, True, True, True, True, True], [False, False, True, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, True, True, True, True, True, True], [False, False, True, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
33. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 0, 0, 0, 0, 0, 1], B=[0, 0, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([True, False, True, True, True, True, True, True], [True, False, True, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, True, True, True, True, True], [True, False, True, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
34. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 0, 0, 0, 0, 0, 1], B=[1, 0, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([True, False, True, True, True, True, True, True], [False, False, True, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, True, True, True, True, True], [False, False, True, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
35. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 0, 0, 0, 0, 0, 1], B=[0, 0, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([False, False, True, True, True, True, True, True], [False, False, True, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, True, True, True, True, True], [False, False, True, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
36. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 0, 0, 0, 0, 0, 1], B=[0, 0, 1, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([True, True, True, True, True, True, True, True], [True, True, False, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [True, True, False, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
37. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 0, 0, 0, 0, 0, 1], B=[1, 0, 1, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([True, True, True, True, True, True, True, True], [False, True, False, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [False, True, False, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
38. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 0, 0, 0, 0, 0, 1], B=[0, 0, 1, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([False, True, True, True, True, True, True, True], [False, True, False, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, True, True, True, True, True, True], [False, True, False, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
39. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 0, 0, 0, 0, 0, 1], B=[0, 1, 1, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([True, True, True, True, True, True, True, True], [True, False, False, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [True, False, False, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
40. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 0, 0, 0, 0, 0, 1], B=[1, 1, 1, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([True, True, True, True, True, True, True, True], [False, False, False, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [False, False, False, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
41. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 0, 0, 0, 0, 0, 1], B=[0, 1, 1, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([False, True, True, True, True, True, True, True], [False, False, False, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, True, True, True, True, True, True], [False, False, False, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
42. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 0, 0, 0, 0, 0, 1], B=[0, 0, 1, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([True, False, True, True, True, True, True, True], [True, False, False, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, True, True, True, True, True], [True, False, False, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
43. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 0, 0, 0, 0, 0, 1], B=[1, 0, 1, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([True, False, True, True, True, True, True, True], [False, False, False, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, True, True, True, True, True], [False, False, False, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
44. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 0, 0, 0, 0, 0, 1], B=[0, 0, 1, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([False, False, True, True, True, True, True, True], [False, False, False, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, True, True, True, True, True], [False, False, False, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
45. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 1, 0, 0, 0, 0, 1], B=[0, 0, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([True, True, False, True, True, True, True, True], [True, True, False, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, True, True, True, True, True], [True, True, False, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
46. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 1, 0, 0, 0, 0, 1], B=[1, 0, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([True, True, False, True, True, True, True, True], [False, True, False, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, True, True, True, True, True], [False, True, False, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
47. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 1, 0, 0, 0, 0, 1], B=[0, 0, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([False, True, False, True, True, True, True, True], [False, True, False, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, True, True, True, True, True], [False, True, False, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
48. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 1, 0, 0, 0, 0, 1], B=[0, 1, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([True, True, False, True, True, True, True, True], [True, False, False, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, True, True, True, True, True], [True, False, False, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
49. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 1, 0, 0, 0, 0, 1], B=[1, 1, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([True, True, False, True, True, True, True, True], [False, False, False, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, True, True, True, True, True], [False, False, False, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
50. Material Implication and Biconditional Tables
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 1, 0, 0, 0, 0, 1], B=[0, 1, 0, 0, 0, 0, 0, 1]. Give (A→B truth table, A↔B truth table).
View answer and explanation
([False, True, False, True, True, True, True, True], [False, False, False, True, True, True, True, True])
Implication is False only for True→False; biconditional requires matching truth values. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, True, True, True, True, True], [False, False, False, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-implication-biconditional · candidate
51. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([True, True, True, True, True, True, True, True], [True, True, True, True, True, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [True, True, True, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
52. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 1, 1, 1, 1, 1, 1, 1]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
53. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 0, 0, 0, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([False, True, True, True, True, True, True, True], [False, True, True, True, True, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, True, True, True, True, True, True], [False, True, True, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
54. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 1, 0, 0, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([True, False, True, True, True, True, True, True], [True, False, True, True, True, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, True, True, True, True, True], [True, False, True, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
55. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 1, 0, 0, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([False, False, True, True, True, True, True, True], [False, False, True, True, True, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, True, True, True, True, True], [False, False, True, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
56. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 0, 1, 0, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([True, True, False, True, True, True, True, True], [True, True, False, True, True, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, True, True, True, True, True], [True, True, False, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
57. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 0, 1, 0, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([False, True, False, True, True, True, True, True], [False, True, False, True, True, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, True, True, True, True, True], [False, True, False, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
58. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 1, 1, 0, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([True, False, False, True, True, True, True, True], [True, False, False, True, True, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, False, True, True, True, True, True], [True, False, False, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
59. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 1, 1, 0, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([False, False, False, True, True, True, True, True], [False, False, False, True, True, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, True, True, True, True, True], [False, False, False, True, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
60. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 0, 0, 1, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([True, True, True, False, True, True, True, True], [True, True, True, False, True, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, False, True, True, True, True], [True, True, True, False, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
61. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 0, 0, 1, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([False, True, True, False, True, True, True, True], [False, True, True, False, True, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, True, False, True, True, True, True], [False, True, True, False, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
62. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 1, 0, 1, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([True, False, True, False, True, True, True, True], [True, False, True, False, True, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, False, True, True, True, True], [True, False, True, False, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
63. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 1, 0, 1, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([False, False, True, False, True, True, True, True], [False, False, True, False, True, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, False, True, True, True, True], [False, False, True, False, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
64. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 0, 1, 1, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([True, True, False, False, True, True, True, True], [True, True, False, False, True, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, False, True, True, True, True], [True, True, False, False, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
65. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 0, 1, 1, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([False, True, False, False, True, True, True, True], [False, True, False, False, True, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, False, True, True, True, True], [False, True, False, False, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
66. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 1, 1, 1, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([True, False, False, False, True, True, True, True], [True, False, False, False, True, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, False, False, True, True, True, True], [True, False, False, False, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
67. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 1, 1, 1, 0, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([False, False, False, False, True, True, True, True], [False, False, False, False, True, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, True, True, True, True], [False, False, False, False, True, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
68. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 0, 0, 0, 1, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([True, True, True, True, False, True, True, True], [True, True, True, True, False, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, False, True, True, True], [True, True, True, True, False, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
69. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 0, 0, 0, 1, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([False, True, True, True, False, True, True, True], [False, True, True, True, False, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, True, True, False, True, True, True], [False, True, True, True, False, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
70. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 1, 0, 0, 1, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([True, False, True, True, False, True, True, True], [True, False, True, True, False, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, True, False, True, True, True], [True, False, True, True, False, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
71. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 1, 0, 0, 1, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([False, False, True, True, False, True, True, True], [False, False, True, True, False, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, True, False, True, True, True], [False, False, True, True, False, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
72. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 0, 1, 0, 1, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([True, True, False, True, False, True, True, True], [True, True, False, True, False, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, True, False, True, True, True], [True, True, False, True, False, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
73. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 0, 1, 0, 1, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([False, True, False, True, False, True, True, True], [False, True, False, True, False, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, True, False, True, True, True], [False, True, False, True, False, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
74. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[0, 1, 1, 0, 1, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([True, False, False, True, False, True, True, True], [True, False, False, True, False, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, False, True, False, True, True, True], [True, False, False, True, False, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
75. Two Complete De Morgan Computations
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 1, 1, 0, 1, 0, 0, 0]. Give (¬(A∧B) truth table, ¬A∨¬B truth table), computing both complete routes.
View answer and explanation
([False, False, False, True, False, True, True, True], [False, False, False, True, False, True, True, True])
One route negates a conjunction; the other negates each input and takes inclusive disjunction. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, True, False, True, True, True], [False, False, False, True, False, True, True, True]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-demorgan-table · candidate
76. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 0, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
77. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 1, 1, 1, 1, 1], B=[1, 1, 1, 1, 1, 1, 1, 1]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([True, True, True, True, True, True, True, True], [False, False, False, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, True, True, True, True, True], [False, False, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
78. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 0, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([True, False, False, False, False, False, False, False], [True, False, False, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, False, False, False, False, False, False], [True, False, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
79. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 0, 0, 0, 0, 0, 0], B=[1, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([True, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, False, False, False, False, False, False], [False, False, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
80. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 0, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([False, True, False, False, False, False, False, False], [False, True, False, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, False, False, False, False, False], [False, True, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
81. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 0, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([True, True, False, False, False, False, False, False], [True, True, False, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, False, False, False, False, False], [True, True, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
82. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 0, 0, 0, 0, 0, 0], B=[1, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([True, True, False, False, False, False, False, False], [False, True, False, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, False, False, False, False, False], [False, True, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
83. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 0, 0, 0, 0, 0, 0], B=[0, 1, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([False, True, False, False, False, False, False, False], [False, False, False, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, False, False, False, False, False, False], [False, False, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
84. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 0, 0, 0, 0, 0, 0], B=[0, 1, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([True, True, False, False, False, False, False, False], [True, False, False, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, False, False, False, False, False], [True, False, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
85. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 0, 0, 0, 0, 0, 0], B=[1, 1, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([True, True, False, False, False, False, False, False], [False, False, False, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, False, False, False, False, False, False], [False, False, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
86. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 1, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([False, False, True, False, False, False, False, False], [False, False, True, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, False, False, False, False, False], [False, False, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
87. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 1, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([True, False, True, False, False, False, False, False], [True, False, True, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, False, False, False, False, False], [True, False, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
88. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 1, 0, 0, 0, 0, 0], B=[1, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([True, False, True, False, False, False, False, False], [False, False, True, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, False, False, False, False, False], [False, False, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
89. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 1, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([False, True, True, False, False, False, False, False], [False, True, True, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, True, False, False, False, False, False], [False, True, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
90. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[0, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([True, True, True, False, False, False, False, False], [True, True, True, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, False, False, False, False, False], [True, True, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
91. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[1, 0, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([True, True, True, False, False, False, False, False], [False, True, True, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, False, False, False, False, False], [False, True, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
92. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 1, 0, 0, 0, 0, 0], B=[0, 1, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([False, True, True, False, False, False, False, False], [False, False, True, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, True, False, False, False, False, False], [False, False, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
93. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[0, 1, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([True, True, True, False, False, False, False, False], [True, False, True, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, False, False, False, False, False], [True, False, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
94. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[1, 1, 0, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([True, True, True, False, False, False, False, False], [False, False, True, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, False, False, False, False, False], [False, False, True, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
95. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 0, 1, 0, 0, 0, 0, 0], B=[0, 0, 1, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([False, False, True, False, False, False, False, False], [False, False, False, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, False, True, False, False, False, False, False], [False, False, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
96. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 1, 0, 0, 0, 0, 0], B=[0, 0, 1, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([True, False, True, False, False, False, False, False], [True, False, False, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, False, False, False, False, False], [True, False, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
97. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 0, 1, 0, 0, 0, 0, 0], B=[1, 0, 1, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([True, False, True, False, False, False, False, False], [False, False, False, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, False, True, False, False, False, False, False], [False, False, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
98. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[0, 1, 1, 0, 0, 0, 0, 0], B=[0, 0, 1, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([False, True, True, False, False, False, False, False], [False, True, False, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([False, True, True, False, False, False, False, False], [False, True, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
99. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[0, 0, 1, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([True, True, True, False, False, False, False, False], [True, True, False, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, False, False, False, False, False], [True, True, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
100. Inclusive Disjunction versus Exactly-One Truth
Complete classical eight-row tables have indices 0,…,7, with 1=True and 0=False: A=[1, 1, 1, 0, 0, 0, 0, 0], B=[1, 0, 1, 0, 0, 0, 0, 0]. Give (inclusive A∨B truth table, exactly-one-True XOR truth table), distinguishing the two.
View answer and explanation
([True, True, True, False, False, False, False, False], [False, True, False, False, False, False, False, False])
Inclusive disjunction allows two True inputs; XOR allows exactly one. Material implication is not causation, and a finite table is not a proof of every inference rule. The exact result, retaining the requested order, is ([True, True, True, False, False, False, False, False], [False, True, False, False, False, False, False, False]).
Reviewed step-by-step derivation
Logical connectives · qf-density13-connectives-inclusion-vs-xor · candidate
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