# Concept derivation guides

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Concept guide



## [Logical connectives: testing ∨, →, ↔ and brackets on divisibility statements](/en/derivations/derivation-mko-logical-connectives-01/?from=%2Fen%2Fderivations%2F%3Fq%3Dmko-logical-connectives)

For an integer n let P(n) be '4∣n' and Q(n) be '2∣n'. (1) Decide the truth of '4∣12 ∨ 6∣12' and explain that disjunction is inclusive; (2) prove ∀n∈ℤ (P(n)→Q(n)); (3) prove that ∀n∈ℤ (Q(n)→P(n)) is false, and hence that ∀n∈ℤ (P(n)↔Q(n)) is false; (4) decide the truth of P(3)→Q(3) and of '2+2=4 → 7 is odd', explaining that implication is not causation; (5) compare the truth of ¬Q(2)∧P(2) and ¬(Q(2)∧P(2)).

Logical connectives

derivation-mko-logical-connectives-01





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