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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Function mapping · qf-density12-mapping-equality-obstruction-list · candidate
Canonical question JSONL · English JSONL · Validation report