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MMLU-Pro / 8974 / Let A and B be sets, f: A -> B and g: B -> A be functions such that for all a…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Let A and B be sets, f: A -> B and g: B -> A be functions such that for all a \in A, g(f(a)) = a. Statement 1 | The function g must necessarily be injective. Statement 2 | The function g must necessarily be surjective.

category

math

options

  1. Not necessarily False, True
  2. True, False
  3. False, True
  4. False, Not necessarily False
  5. True, Not necessarily False
  6. True, True
  7. Not necessarily True, True
  8. False, False
  9. Not necessarily True, False
  10. True, Not necessarily True

src

ori_mmlu-abstract_algebra

Discussion

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Source and history

upstream_id / Original problem ID
8974
task_id
13f93913-804e-5587-aca1-dd88eea1aeec
task_key
default--test--8974
task_revision_id
1
config / split
default / test

Official source

initial import