# Complete Typed Maps, Ranges, and Query Guards

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-20261012-r07-function-mapping-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 Ordered Finite Mapping Graph

The complete total map f:Fin(0)→Fin(0) has images=[] indexed from 0; Fin(0)=∅. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0001/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 2. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(1)→Fin(1) has images=[0] indexed from 0; Fin(1)={0,…,0}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 0]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 0]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0002/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 3. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[2, 0, 5] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 2], [1, 0], [2, 5]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 2], [1, 0], [2, 5]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0003/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 4. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[3, 0, 6] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 3], [1, 0], [2, 6]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 3], [1, 0], [2, 6]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0004/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 5. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[4, 0, 7] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 4], [1, 0], [2, 7]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 4], [1, 0], [2, 7]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0005/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 6. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[5, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 5], [1, 0], [2, 0]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 5], [1, 0], [2, 0]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0006/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 7. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[6, 0, 1] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 6], [1, 0], [2, 1]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 6], [1, 0], [2, 1]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0007/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 8. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[7, 0, 2] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 7], [1, 0], [2, 2]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 7], [1, 0], [2, 2]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0008/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 9. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[0, 1, 3] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 0], [1, 1], [2, 3]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 0], [1, 1], [2, 3]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0009/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 10. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[1, 1, 4] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 1], [1, 1], [2, 4]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 1], [1, 1], [2, 4]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0010/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 11. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[2, 1, 5] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 2], [1, 1], [2, 5]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 2], [1, 1], [2, 5]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0011/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 12. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[3, 1, 6] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 3], [1, 1], [2, 6]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 3], [1, 1], [2, 6]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0012/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 13. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[4, 1, 7] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 4], [1, 1], [2, 7]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 4], [1, 1], [2, 7]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0013/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 14. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[5, 1, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 5], [1, 1], [2, 0]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 5], [1, 1], [2, 0]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0014/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 15. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[6, 1, 1] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 6], [1, 1], [2, 1]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 6], [1, 1], [2, 1]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0015/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 16. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[7, 1, 2] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 7], [1, 1], [2, 2]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 7], [1, 1], [2, 2]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0016/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 17. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[0, 2, 3] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 0], [1, 2], [2, 3]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 0], [1, 2], [2, 3]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0017/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 18. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[1, 2, 4] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 1], [1, 2], [2, 4]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 1], [1, 2], [2, 4]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0018/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 19. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[2, 2, 5] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 2], [1, 2], [2, 5]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 2], [1, 2], [2, 5]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0019/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 20. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[3, 2, 6] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 3], [1, 2], [2, 6]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 3], [1, 2], [2, 6]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0020/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 21. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[4, 2, 7] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 4], [1, 2], [2, 7]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 4], [1, 2], [2, 7]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0021/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 22. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[5, 2, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 5], [1, 2], [2, 0]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 5], [1, 2], [2, 0]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0022/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 23. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[6, 2, 1] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 6], [1, 2], [2, 1]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 6], [1, 2], [2, 1]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0023/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 24. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[7, 2, 2] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 7], [1, 2], [2, 2]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 7], [1, 2], [2, 2]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0024/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 25. Complete Ordered Finite Mapping Graph

The complete total map f:Fin(3)→Fin(8) has images=[0, 3, 3] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. List every [i,f(i)] in source-index order, using [] for an empty source.

View answer and explanation[[0, 0], [1, 3], [2, 3]]

Read the one output for every legal input; do not fabricate graph pairs to use the whole codomain. This is a total mathematical map, not a partial program function. The exact result, retaining the requested order, is [[0, 0], [1, 3], [2, 3]].



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0025/)

Function mapping · qf-density12-mapping-full-graph · candidate





## 26. Actual Range and Unused Codomain

The complete total map f:Fin(0)→Fin(0) has images=[] indexed from 0; Fin(0)=∅. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

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

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0026/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 27. Actual Range and Unused Codomain

The complete total map f:Fin(0)→Fin(1) has images=[] indexed from 0; Fin(0)=∅. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([], [0], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([], [0], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0027/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 28. Actual Range and Unused Codomain

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([0, 1], [], Yes)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 1], [], Yes).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0028/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 29. Actual Range and Unused Codomain

The complete total map f:Fin(1)→Fin(8) has images=[0] indexed from 0; Fin(1)={0,…,0}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([0], [1, 2, 3, 4, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0], [1, 2, 3, 4, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0029/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 30. Actual Range and Unused Codomain

The complete total map f:Fin(1)→Fin(8) has images=[1] indexed from 0; Fin(1)={0,…,0}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([1], [0, 2, 3, 4, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([1], [0, 2, 3, 4, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0030/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 31. Actual Range and Unused Codomain

The complete total map f:Fin(2)→Fin(8) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([0, 1], [2, 3, 4, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 1], [2, 3, 4, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0031/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 32. Actual Range and Unused Codomain

The complete total map f:Fin(1)→Fin(8) has images=[2] indexed from 0; Fin(1)={0,…,0}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([2], [0, 1, 3, 4, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([2], [0, 1, 3, 4, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0032/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 33. Actual Range and Unused Codomain

The complete total map f:Fin(2)→Fin(8) has images=[0, 2] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([0, 2], [1, 3, 4, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 2], [1, 3, 4, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0033/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 34. Actual Range and Unused Codomain

The complete total map f:Fin(2)→Fin(8) has images=[1, 2] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([1, 2], [0, 3, 4, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([1, 2], [0, 3, 4, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0034/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 35. Actual Range and Unused Codomain

The complete total map f:Fin(3)→Fin(8) has images=[0, 1, 2] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([0, 1, 2], [3, 4, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 1, 2], [3, 4, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0035/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 36. Actual Range and Unused Codomain

The complete total map f:Fin(1)→Fin(8) has images=[3] indexed from 0; Fin(1)={0,…,0}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([3], [0, 1, 2, 4, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([3], [0, 1, 2, 4, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0036/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 37. Actual Range and Unused Codomain

The complete total map f:Fin(2)→Fin(8) has images=[0, 3] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([0, 3], [1, 2, 4, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 3], [1, 2, 4, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0037/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 38. Actual Range and Unused Codomain

The complete total map f:Fin(2)→Fin(8) has images=[1, 3] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([1, 3], [0, 2, 4, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([1, 3], [0, 2, 4, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0038/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 39. Actual Range and Unused Codomain

The complete total map f:Fin(3)→Fin(8) has images=[0, 1, 3] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([0, 1, 3], [2, 4, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 1, 3], [2, 4, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0039/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 40. Actual Range and Unused Codomain

The complete total map f:Fin(2)→Fin(8) has images=[2, 3] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([2, 3], [0, 1, 4, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([2, 3], [0, 1, 4, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0040/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 41. Actual Range and Unused Codomain

The complete total map f:Fin(3)→Fin(8) has images=[0, 2, 3] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([0, 2, 3], [1, 4, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 2, 3], [1, 4, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0041/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 42. Actual Range and Unused Codomain

The complete total map f:Fin(3)→Fin(8) has images=[1, 2, 3] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([1, 2, 3], [0, 4, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([1, 2, 3], [0, 4, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0042/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 43. Actual Range and Unused Codomain

The complete total map f:Fin(4)→Fin(8) has images=[0, 1, 2, 3] indexed from 0; Fin(4)={0,…,3}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([0, 1, 2, 3], [4, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 1, 2, 3], [4, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0043/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 44. Actual Range and Unused Codomain

The complete total map f:Fin(1)→Fin(8) has images=[4] indexed from 0; Fin(1)={0,…,0}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([4], [0, 1, 2, 3, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([4], [0, 1, 2, 3, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0044/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 45. Actual Range and Unused Codomain

The complete total map f:Fin(2)→Fin(8) has images=[0, 4] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([0, 4], [1, 2, 3, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 4], [1, 2, 3, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0045/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 46. Actual Range and Unused Codomain

The complete total map f:Fin(2)→Fin(8) has images=[1, 4] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([1, 4], [0, 2, 3, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([1, 4], [0, 2, 3, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0046/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 47. Actual Range and Unused Codomain

The complete total map f:Fin(3)→Fin(8) has images=[0, 1, 4] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([0, 1, 4], [2, 3, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 1, 4], [2, 3, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0047/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 48. Actual Range and Unused Codomain

The complete total map f:Fin(2)→Fin(8) has images=[2, 4] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([2, 4], [0, 1, 3, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([2, 4], [0, 1, 3, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0048/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 49. Actual Range and Unused Codomain

The complete total map f:Fin(3)→Fin(8) has images=[0, 2, 4] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([0, 2, 4], [1, 3, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([0, 2, 4], [1, 3, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0049/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 50. Actual Range and Unused Codomain

The complete total map f:Fin(3)→Fin(8) has images=[1, 2, 4] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. Give (increasing actual range, increasing unused codomain elements, does the range equal the entire codomain?).

View answer and explanation([1, 2, 4], [0, 3, 5, 6, 7], No)

Deduplicate all outputs, then enumerate unused codomain elements; total definition alone does not imply surjectivity. The exact result, retaining the requested order, is ([1, 2, 4], [0, 3, 5, 6, 7], No).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0050/)

Function mapping · qf-density12-mapping-range-codomain-defect · candidate





## 51. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(0)→Fin(0) has images=[] indexed from 0; Fin(0)=∅. Every table entry must lie in the target type. Ordered queries=[-1, 0, 1]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([No, No, No], [ill-typed, ill-typed, ill-typed])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([No, No, No], [ill-typed, ill-typed, ill-typed]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0051/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 52. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[1, 101, 102]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([Yes, No, No], [1, ill-typed, ill-typed])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, No, No], [1, ill-typed, ill-typed]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0052/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 53. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[0, 0, 102]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([Yes, Yes, No], [0, 0, ill-typed])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, No], [0, 0, ill-typed]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0053/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 54. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[1, 0, 102]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([Yes, Yes, No], [1, 0, ill-typed])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, No], [1, 0, ill-typed]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0054/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 55. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[100, 1, 102]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([No, Yes, No], [ill-typed, 1, ill-typed])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([No, Yes, No], [ill-typed, 1, ill-typed]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0055/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 56. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[0, 1, 102]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([Yes, Yes, No], [0, 1, ill-typed])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, No], [0, 1, ill-typed]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0056/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 57. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[1, 1, 102]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([Yes, Yes, No], [1, 1, ill-typed])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, No], [1, 1, ill-typed]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0057/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 58. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[100, 101, 0]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([No, No, Yes], [ill-typed, ill-typed, 0])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([No, No, Yes], [ill-typed, ill-typed, 0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0058/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 59. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[0, 101, 0]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([Yes, No, Yes], [0, ill-typed, 0])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, No, Yes], [0, ill-typed, 0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0059/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 60. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[1, 101, 0]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([Yes, No, Yes], [1, ill-typed, 0])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, No, Yes], [1, ill-typed, 0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0060/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 61. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[100, 0, 0]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([No, Yes, Yes], [ill-typed, 0, 0])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([No, Yes, Yes], [ill-typed, 0, 0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0061/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 62. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[0, 0, 0]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([Yes, Yes, Yes], [0, 0, 0])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [0, 0, 0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0062/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 63. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[1, 0, 0]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([Yes, Yes, Yes], [1, 0, 0])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [1, 0, 0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0063/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 64. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[100, 1, 0]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([No, Yes, Yes], [ill-typed, 1, 0])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([No, Yes, Yes], [ill-typed, 1, 0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0064/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 65. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[0, 1, 0]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([Yes, Yes, Yes], [0, 1, 0])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [0, 1, 0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0065/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 66. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[1, 1, 0]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([Yes, Yes, Yes], [1, 1, 0])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [1, 1, 0]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0066/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 67. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[100, 101, 1]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([No, No, Yes], [ill-typed, ill-typed, 1])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([No, No, Yes], [ill-typed, ill-typed, 1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0067/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 68. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[0, 101, 1]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([Yes, No, Yes], [0, ill-typed, 1])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, No, Yes], [0, ill-typed, 1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0068/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 69. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[1, 101, 1]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([Yes, No, Yes], [1, ill-typed, 1])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, No, Yes], [1, ill-typed, 1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0069/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 70. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[100, 0, 1]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([No, Yes, Yes], [ill-typed, 0, 1])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([No, Yes, Yes], [ill-typed, 0, 1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0070/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 71. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[0, 0, 1]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([Yes, Yes, Yes], [0, 0, 1])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [0, 0, 1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0071/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 72. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[1, 0, 1]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([Yes, Yes, Yes], [1, 0, 1])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [1, 0, 1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0072/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 73. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[100, 1, 1]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([No, Yes, Yes], [ill-typed, 1, 1])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([No, Yes, Yes], [ill-typed, 1, 1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0073/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 74. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[0, 1, 1]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

View answer and explanation([Yes, Yes, Yes], [0, 1, 1])

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [0, 1, 1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0074/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 75. Typed Candidate Evaluation of a Total Map

The complete total map f:Fin(2)→Fin(2) has images=[0, 1] indexed from 0; Fin(2)={0,…,1}. Every table entry must lie in the target type. Ordered queries=[1, 1, 1]. Give (legal-source-type mask, outputs for typed queries or ill-typed); do not evaluate f outside its source type.

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

Check the source index before reading the table; an outside-type candidate is not an undefined input of this total function. The exact result, retaining the requested order, is ([Yes, Yes, Yes], [1, 1, 1]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0075/)

Function mapping · qf-density12-mapping-candidate-evaluation · candidate





## 76. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(0)→Fin(0) has images=[] indexed from 0; Fin(0)=∅. Every table entry must lie in the target type. A second complete total map g on the same types has other=[]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([], [])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([], []).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0076/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 77. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[0, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[1, 0, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([0], [[0, 1]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([0], [[0, 1]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0077/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 78. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[0, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 1, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([1], [[0, 1]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([1], [[0, 1]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0078/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 79. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[0, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 0, 1]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([2], [[0, 1]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([2], [[0, 1]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0079/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 80. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[1, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[2, 0, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([0], [[1, 2]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([0], [[1, 2]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0080/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 81. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[0, 1, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 2, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([1], [[1, 2]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([1], [[1, 2]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0081/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 82. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[0, 0, 1] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 0, 2]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([2], [[1, 2]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([2], [[1, 2]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0082/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 83. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[2, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[3, 0, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([0], [[2, 3]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([0], [[2, 3]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0083/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 84. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[0, 2, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 3, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([1], [[2, 3]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([1], [[2, 3]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0084/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 85. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[0, 0, 2] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 0, 3]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([2], [[2, 3]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([2], [[2, 3]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0085/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 86. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[3, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[4, 0, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([0], [[3, 4]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([0], [[3, 4]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0086/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 87. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[0, 3, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 4, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([1], [[3, 4]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([1], [[3, 4]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0087/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 88. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[0, 0, 3] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 0, 4]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([2], [[3, 4]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([2], [[3, 4]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0088/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 89. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[4, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[5, 0, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([0], [[4, 5]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([0], [[4, 5]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0089/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 90. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[0, 4, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 5, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([1], [[4, 5]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([1], [[4, 5]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0090/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 91. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[0, 0, 4] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 0, 5]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([2], [[4, 5]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([2], [[4, 5]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0091/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 92. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[5, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[6, 0, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([0], [[5, 6]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([0], [[5, 6]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0092/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 93. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[0, 5, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 6, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([1], [[5, 6]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([1], [[5, 6]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0093/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 94. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[0, 0, 5] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 0, 6]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([2], [[5, 6]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([2], [[5, 6]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0094/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 95. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[6, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[7, 0, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([0], [[6, 7]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([0], [[6, 7]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0095/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 96. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[0, 6, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 7, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([1], [[6, 7]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([1], [[6, 7]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0096/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 97. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[0, 0, 6] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 0, 7]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([2], [[6, 7]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([2], [[6, 7]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0097/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 98. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[7, 0, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 0, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([0], [[7, 0]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([0], [[7, 0]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0098/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 99. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[0, 7, 0] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 0, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([1], [[7, 0]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([1], [[7, 0]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0099/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate





## 100. Complete Mapping Mismatch Indices and Ordered Values

The complete total map f:Fin(3)→Fin(8) has images=[0, 0, 7] indexed from 0; Fin(3)={0,…,2}. Every table entry must lie in the target type. A second complete total map g on the same types has other=[0, 0, 0]. Give (increasing mismatch indices, aligned [f(i),g(i)] value pairs).

View answer and explanation([2], [[7, 0]])

Check both complete tables’ typing, then compare every source point; retain only mismatches and do not exchange the ordered value pairs. The exact result, retaining the requested order, is ([2], [[7, 0]]).



[Reviewed step-by-step derivation](https://ocme.evemisslab.com/en/questions/q-20261008-advance-20261012-r07-function-mapping-0100/)

Function mapping · qf-density12-mapping-equality-obstruction-list · candidate



[Canonical question JSONL](https://ocme.evemisslab.com/data/questions/batches/batch-20261008-advance-20261012-r07-function-mapping-foundations/questions.jsonl) · [English JSONL](https://ocme.evemisslab.com/data/i18n/questions/batch-20261008-advance-20261012-r07-function-mapping-foundations.en.jsonl) · [Validation report](https://ocme.evemisslab.com/data/questions/batches/batch-20261008-advance-20261012-r07-function-mapping-foundations/validation-report.json)