# Inclusion Obstructions and Strictness Witnesses

This batch has passed Schema, deduplication, source-snapshot, and independent-answer recomputation checks; it is still not marked as human-reviewed.

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-20261008-advance-20261011-r05-subset-foundations · 2026-10-08 · 100 questions

This English edition is an AI candidate and does not yet have an OCME Atlas (GPT-6) Twin closure receipt.



## 1. Complete Inclusion Obstruction Set

Finite integer sets A=[] and B=[1]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0001/)

Subset · qf-density11-subset-obstruction-list · candidate





## 2. Complete Inclusion Obstruction Set

Finite integer sets A=[-1] and B=[]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-1]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-1].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0002/)

Subset · qf-density11-subset-obstruction-list · candidate





## 3. Complete Inclusion Obstruction Set

Finite integer sets A=[-2, 2, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-2, 2]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-2, 2].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0003/)

Subset · qf-density11-subset-obstruction-list · candidate





## 4. Complete Inclusion Obstruction Set

Finite integer sets A=[-3, 3, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-3, 3]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-3, 3].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0004/)

Subset · qf-density11-subset-obstruction-list · candidate





## 5. Complete Inclusion Obstruction Set

Finite integer sets A=[-4, 4, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-4, 4]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-4, 4].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0005/)

Subset · qf-density11-subset-obstruction-list · candidate





## 6. Complete Inclusion Obstruction Set

Finite integer sets A=[-5, 5, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-5, 5]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-5, 5].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0006/)

Subset · qf-density11-subset-obstruction-list · candidate





## 7. Complete Inclusion Obstruction Set

Finite integer sets A=[-6, 6, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-6, 6]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-6, 6].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0007/)

Subset · qf-density11-subset-obstruction-list · candidate





## 8. Complete Inclusion Obstruction Set

Finite integer sets A=[-7, 7, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-7, 7]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-7, 7].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0008/)

Subset · qf-density11-subset-obstruction-list · candidate





## 9. Complete Inclusion Obstruction Set

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.

View answer and explanation[-8, 8]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-8, 8].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0009/)

Subset · qf-density11-subset-obstruction-list · candidate





## 10. Complete Inclusion Obstruction Set

Finite integer sets A=[-9, 9, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-9, 9]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-9, 9].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0010/)

Subset · qf-density11-subset-obstruction-list · candidate





## 11. Complete Inclusion Obstruction Set

Finite integer sets A=[-10, 10, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-10, 10]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-10, 10].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0011/)

Subset · qf-density11-subset-obstruction-list · candidate





## 12. Complete Inclusion Obstruction Set

Finite integer sets A=[-11, 11, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-11, 11]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-11, 11].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0012/)

Subset · qf-density11-subset-obstruction-list · candidate





## 13. Complete Inclusion Obstruction Set

Finite integer sets A=[-12, 12, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-12, 12]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-12, 12].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0013/)

Subset · qf-density11-subset-obstruction-list · candidate





## 14. Complete Inclusion Obstruction Set

Finite integer sets A=[-13, 13, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-13, 13]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-13, 13].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0014/)

Subset · qf-density11-subset-obstruction-list · candidate





## 15. Complete Inclusion Obstruction Set

Finite integer sets A=[-14, 14, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-14, 14]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-14, 14].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0015/)

Subset · qf-density11-subset-obstruction-list · candidate





## 16. Complete Inclusion Obstruction Set

Finite integer sets A=[-15, 15, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-15, 15]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-15, 15].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0016/)

Subset · qf-density11-subset-obstruction-list · candidate





## 17. Complete Inclusion Obstruction Set

Finite integer sets A=[-16, 16, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-16, 16]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-16, 16].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0017/)

Subset · qf-density11-subset-obstruction-list · candidate





## 18. Complete Inclusion Obstruction Set

Finite integer sets A=[-17, 17, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-17, 17]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-17, 17].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0018/)

Subset · qf-density11-subset-obstruction-list · candidate





## 19. Complete Inclusion Obstruction Set

Finite integer sets A=[-18, 18, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-18, 18]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-18, 18].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0019/)

Subset · qf-density11-subset-obstruction-list · candidate





## 20. Complete Inclusion Obstruction Set

Finite integer sets A=[-19, 19, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-19, 19]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-19, 19].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0020/)

Subset · qf-density11-subset-obstruction-list · candidate





## 21. Complete Inclusion Obstruction Set

Finite integer sets A=[-20, 20, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-20, 20]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-20, 20].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0021/)

Subset · qf-density11-subset-obstruction-list · candidate





## 22. Complete Inclusion Obstruction Set

Finite integer sets A=[-21, 21, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-21, 21]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-21, 21].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0022/)

Subset · qf-density11-subset-obstruction-list · candidate





## 23. Complete Inclusion Obstruction Set

Finite integer sets A=[-22, 22, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-22, 22]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-22, 22].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0023/)

Subset · qf-density11-subset-obstruction-list · candidate





## 24. Complete Inclusion Obstruction Set

Finite integer sets A=[-23, 23, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-23, 23]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-23, 23].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0024/)

Subset · qf-density11-subset-obstruction-list · candidate





## 25. Complete Inclusion Obstruction Set

Finite integer sets A=[-24, 24, 0] and B=[0]; repeated elements count once. List all obstructions to A⊆B, namely elements in A but not B, increasingly without repetition.

View answer and explanation[-24, 24]

The obstruction set is A\B; inclusion holds exactly when it is empty, and an empty A supplies no counterexample. The exact result, retaining the requested order, is [-24, 24].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0025/)

Subset · qf-density11-subset-obstruction-list · candidate





## 26. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[0] and B=[0]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(Yes, No, [], [])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (Yes, No, [], []).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0026/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 27. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[] and B=[-1]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(Yes, Yes, [], [-1])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (Yes, Yes, [], [-1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0027/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 28. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[-2] and B=[]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(No, No, [-2], [])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-2], []).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0028/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 29. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[0] and B=[0, 3]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(Yes, Yes, [], [3])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (Yes, Yes, [], [3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0029/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 30. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[-4, 0] and B=[0]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(No, No, [-4], [])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-4], []).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0030/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 31. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[-5, 0] and B=[0, 5]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(No, No, [-5], [5])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-5], [5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0031/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 32. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[0] and B=[0, 6]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(Yes, Yes, [], [6])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (Yes, Yes, [], [6]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0032/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 33. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[-7, 0] and B=[0]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(No, No, [-7], [])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-7], []).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0033/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 34. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[-8, 0] and B=[0, 8]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(No, No, [-8], [8])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-8], [8]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0034/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 35. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[0] and B=[0, 9]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(Yes, Yes, [], [9])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (Yes, Yes, [], [9]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0035/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 36. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[-10, 0] and B=[0]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(No, No, [-10], [])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-10], []).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0036/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 37. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[-11, 0] and B=[0, 11]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(No, No, [-11], [11])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-11], [11]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0037/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 38. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[0] and B=[0, 12]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(Yes, Yes, [], [12])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (Yes, Yes, [], [12]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0038/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 39. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[-13, 0] and B=[0]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(No, No, [-13], [])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-13], []).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0039/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 40. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[-14, 0] and B=[0, 14]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(No, No, [-14], [14])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-14], [14]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0040/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 41. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[0] and B=[0, 15]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(Yes, Yes, [], [15])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (Yes, Yes, [], [15]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0041/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 42. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[-16, 0] and B=[0]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(No, No, [-16], [])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-16], []).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0042/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 43. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[-17, 0] and B=[0, 17]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(No, No, [-17], [17])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-17], [17]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0043/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 44. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[0] and B=[0, 18]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(Yes, Yes, [], [18])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (Yes, Yes, [], [18]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0044/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 45. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[-19, 0] and B=[0]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(No, No, [-19], [])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-19], []).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0045/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 46. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[-20, 0] and B=[0, 20]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(No, No, [-20], [20])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-20], [20]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0046/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 47. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[0] and B=[0, 21]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(Yes, Yes, [], [21])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (Yes, Yes, [], [21]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0047/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 48. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[-22, 0] and B=[0]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(No, No, [-22], [])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-22], []).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0048/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 49. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[-23, 0] and B=[0, 23]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(No, No, [-23], [23])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (No, No, [-23], [23]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0049/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 50. Non-Strict and Strict Inclusion Witnesses

Finite integer sets A=[0] and B=[0, 24]; repeated elements count once. Give (does A⊆B?, does A⊊B?, A\B, B\A), with both witness sets increasing.

View answer and explanation(Yes, Yes, [], [24])

An empty left difference permits inclusion; strict inclusion additionally requires a nonempty right difference. Equal sets pass only the non-strict field. The exact result, retaining the requested order, is (Yes, Yes, [], [24]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0050/)

Subset · qf-density11-subset-strict-witnesses · candidate





## 51. Three Ordered Inclusion Obstructions

Finite integer sets A=[] and B=[0]; repeated elements count once. C=[0, 1] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([], [], [])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([], [], []).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0051/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 52. Three Ordered Inclusion Obstructions

Finite integer sets A=[1] and B=[]; repeated elements count once. C=[1] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([1], [], [])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([1], [], []).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0052/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 53. Three Ordered Inclusion Obstructions

Finite integer sets A=[0] and B=[0, 2]; repeated elements count once. C=[0] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([], [2], [])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([], [2], []).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0053/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 54. Three Ordered Inclusion Obstructions

Finite integer sets A=[-3, 0] and B=[0, 3]; repeated elements count once. C=[0, 4] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-3], [3], [-3])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-3], [3], [-3]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0054/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 55. Three Ordered Inclusion Obstructions

Finite integer sets A=[-4, 0] and B=[0, 4]; repeated elements count once. C=[0, 5] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-4], [4], [-4])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-4], [4], [-4]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0055/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 56. Three Ordered Inclusion Obstructions

Finite integer sets A=[-5, 0] and B=[0, 5]; repeated elements count once. C=[0, 6] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-5], [5], [-5])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-5], [5], [-5]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0056/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 57. Three Ordered Inclusion Obstructions

Finite integer sets A=[-6, 0] and B=[0, 6]; repeated elements count once. C=[0, 7] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-6], [6], [-6])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-6], [6], [-6]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0057/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 58. Three Ordered Inclusion Obstructions

Finite integer sets A=[-7, 0] and B=[0, 7]; repeated elements count once. C=[0, 8] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-7], [7], [-7])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-7], [7], [-7]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0058/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 59. Three Ordered Inclusion Obstructions

Finite integer sets A=[-8, 0] and B=[0, 8]; repeated elements count once. C=[0, 9] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-8], [8], [-8])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-8], [8], [-8]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0059/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 60. Three Ordered Inclusion Obstructions

Finite integer sets A=[-9, 0] and B=[0, 9]; repeated elements count once. C=[0, 10] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-9], [9], [-9])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-9], [9], [-9]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0060/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 61. Three Ordered Inclusion Obstructions

Finite integer sets A=[-10, 0] and B=[0, 10]; repeated elements count once. C=[0, 11] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-10], [10], [-10])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-10], [10], [-10]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0061/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 62. Three Ordered Inclusion Obstructions

Finite integer sets A=[-11, 0] and B=[0, 11]; repeated elements count once. C=[0, 12] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-11], [11], [-11])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-11], [11], [-11]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0062/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 63. Three Ordered Inclusion Obstructions

Finite integer sets A=[-12, 0] and B=[0, 12]; repeated elements count once. C=[0, 13] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-12], [12], [-12])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-12], [12], [-12]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0063/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 64. Three Ordered Inclusion Obstructions

Finite integer sets A=[-13, 0] and B=[0, 13]; repeated elements count once. C=[0, 14] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-13], [13], [-13])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-13], [13], [-13]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0064/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 65. Three Ordered Inclusion Obstructions

Finite integer sets A=[-14, 0] and B=[0, 14]; repeated elements count once. C=[0, 15] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-14], [14], [-14])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-14], [14], [-14]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0065/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 66. Three Ordered Inclusion Obstructions

Finite integer sets A=[-15, 0] and B=[0, 15]; repeated elements count once. C=[0, 16] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-15], [15], [-15])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-15], [15], [-15]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0066/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 67. Three Ordered Inclusion Obstructions

Finite integer sets A=[-16, 0] and B=[0, 16]; repeated elements count once. C=[0, 17] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-16], [16], [-16])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-16], [16], [-16]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0067/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 68. Three Ordered Inclusion Obstructions

Finite integer sets A=[-17, 0] and B=[0, 17]; repeated elements count once. C=[0, 18] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-17], [17], [-17])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-17], [17], [-17]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0068/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 69. Three Ordered Inclusion Obstructions

Finite integer sets A=[-18, 0] and B=[0, 18]; repeated elements count once. C=[0, 19] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-18], [18], [-18])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-18], [18], [-18]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0069/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 70. Three Ordered Inclusion Obstructions

Finite integer sets A=[-19, 0] and B=[0, 19]; repeated elements count once. C=[0, 20] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-19], [19], [-19])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-19], [19], [-19]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0070/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 71. Three Ordered Inclusion Obstructions

Finite integer sets A=[-20, 0] and B=[0, 20]; repeated elements count once. C=[0, 21] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-20], [20], [-20])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-20], [20], [-20]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0071/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 72. Three Ordered Inclusion Obstructions

Finite integer sets A=[-21, 0] and B=[0, 21]; repeated elements count once. C=[0, 22] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-21], [21], [-21])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-21], [21], [-21]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0072/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 73. Three Ordered Inclusion Obstructions

Finite integer sets A=[-22, 0] and B=[0, 22]; repeated elements count once. C=[0, 23] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-22], [22], [-22])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-22], [22], [-22]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0073/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 74. Three Ordered Inclusion Obstructions

Finite integer sets A=[-23, 0] and B=[0, 23]; repeated elements count once. C=[0, 24] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-23], [23], [-23])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-23], [23], [-23]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0074/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 75. Three Ordered Inclusion Obstructions

Finite integer sets A=[-24, 0] and B=[0, 24]; repeated elements count once. C=[0, 25] uses the same integer type. Give (A\B, B\C, A\C), each increasing, retaining empty parts.

View answer and explanation([-24], [24], [-24])

Enumerate each difference independently; a failed link does not automatically decide another difference, and the three fields are not interchangeable. The exact result, retaining the requested order, is ([-24], [24], [-24]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0075/)

Subset · qf-density11-subset-chain-obstructions · candidate





## 76. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[] and B=[]; repeated elements count once. Ordered candidates=[100, 101, 102]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[No, No, No]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, No, No].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0076/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 77. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[-1, 101, 102]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[Yes, No, No]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [Yes, No, No].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0077/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 78. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[1, 2, 102]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[No, No, No]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, No, No].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0078/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 79. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[-1, 2, 102]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[Yes, No, No]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [Yes, No, No].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0079/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 80. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[100, -2, 102]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[No, Yes, No]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, Yes, No].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0080/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 81. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[1, -2, 102]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[No, Yes, No]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, Yes, No].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0081/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 82. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[-1, -2, 102]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[Yes, Yes, No]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [Yes, Yes, No].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0082/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 83. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[100, 101, 3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[No, No, No]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, No, No].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0083/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 84. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[1, 101, 3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[No, No, No]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, No, No].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0084/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 85. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[-1, 101, 3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[Yes, No, No]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [Yes, No, No].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0085/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 86. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[100, 2, 3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[No, No, No]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, No, No].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0086/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 87. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[1, 2, 3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[No, No, No]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, No, No].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0087/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 88. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[-1, 2, 3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[Yes, No, No]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [Yes, No, No].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0088/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 89. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[100, -2, 3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[No, Yes, No]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, Yes, No].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0089/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 90. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[1, -2, 3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[No, Yes, No]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, Yes, No].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0090/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 91. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[-1, -2, 3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[Yes, Yes, No]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [Yes, Yes, No].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0091/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 92. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[100, 101, -3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[No, No, Yes]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, No, Yes].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0092/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 93. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[1, 101, -3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[No, No, Yes]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, No, Yes].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0093/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 94. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[-1, 101, -3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[Yes, No, Yes]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [Yes, No, Yes].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0094/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 95. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[100, 2, -3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[No, No, Yes]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, No, Yes].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0095/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 96. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[1, 2, -3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[No, No, Yes]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, No, Yes].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0096/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 97. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[-1, 2, -3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[Yes, No, Yes]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [Yes, No, Yes].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0097/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 98. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[100, -2, -3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[No, Yes, Yes]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, Yes, Yes].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0098/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 99. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[1, 2, 3]; repeated elements count once. Ordered candidates=[1, -2, -3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[No, Yes, Yes]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [No, Yes, Yes].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0099/)

Subset · qf-density11-subset-candidate-witness-mask · candidate





## 100. Candidate Inclusion-Counterexample Mask

Finite integer sets A=[-3, -2, -1, 1, 2, 3] and B=[]; repeated elements count once. Ordered candidates=[-1, -2, -3]. For each c, answer whether c∈A and c∉B; a candidate outside A cannot be an obstruction.

View answer and explanation[Yes, Yes, Yes]

Require membership in A before excluding membership in B; shared elements and outside-A elements are not counterexamples. The exact result, retaining the requested order, is [Yes, Yes, Yes].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261011-r05-subset-0100/)

Subset · qf-density11-subset-candidate-witness-mask · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261008-advance-20261011-r05-subset-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261008-advance-20261011-r05-subset-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261008-advance-20261011-r05-subset-foundations/validation-report.json)