Explore related knowledge and questions →
← Question derivation index · Original question batch
R0009-05159 · q-20261008-advance-20261011-r05-subset-0009
Finite integer sets A=[-8, 8, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.
G001 — Finite integer sets A=[-8, 8, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate.
Before
A=[-8, 0, 8];B=[0];same integer type
After
A⊆B means every A-element belongs to B
Conditions: none
An inclusion obstruction must belong to A but not B;an element outside A is no witness,and empty A gives no obstruction.
Rule: set_inclusion_definition · Uses: G001
Before
A\B:source element=-8;target=[0]
After
obstruction=Yes
Conditions: none
Audit every source-set element;list it as an obstruction exactly when the target omits it.
Rule: inclusion_obstruction_row · Uses: G001, S001
Before
A\B:source element=0;target=[0]
After
obstruction=No
Conditions: none
Audit every source-set element;list it as an obstruction exactly when the target omits it.
Rule: inclusion_obstruction_row · Uses: G001, S002
Before
A\B:source element=8;target=[0]
After
obstruction=Yes
Conditions: none
Audit every source-set element;list it as an obstruction exactly when the target omits it.
Rule: inclusion_obstruction_row · Uses: G001, S003
Before
[-8, 8]
After
A⊆B=No
Conditions: none
Because every A-element was checked,the empty obstruction set is equivalent to this finite inclusion.
Rule: complete_inclusion_obstruction_inventory · Uses: G001, S004
S005 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S004 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S003 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S002 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.S001 · premise_and_result_audit — Check against the original data and this step's premises; a one-way implication is not an equivalence.[-8, 8]
The full substitutions and premise checks give the original answer; source identity,format and status are unchanged.
Review date: 2026-10-26
Original questions, answers, step expressions, numeric ASTs and historical records are retained. Source candidate labels remain historical and are not overwritten as formal proof.
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: d94c05a7df794f3b5dbb9efe3f6e45b824480e69d656468ec2483df97661fa68candidate record SHA-256: 91b330a3387d978247d9cf1e9d429db1e4ecf6f151df6ee4af99e435e4f9246csemantic review receipt SHA-256: 71e7db519df31f3a164533e472e293cb64f001b475a8d002b4a5c2740a237b56question-first witness SHA-256: 5a43f4f81b6256281f8d139a4010bbde127be803c528e5878857269c8f854462Lean: NOT_RUN · human review: NOT_PERFORMED