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MMLU-Pro / 8540 / 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 f must necessarily be injective. Statement 2 | The function f must necessarily be surjective.

category

math

options

  1. Statement 1 is true for some sets A and B, but false for others
  2. True, True
  3. Statement 2 is false for some sets A and B, but true for others
  4. False, True
  5. Both statements are partially true
  6. False, False
  7. Statement 1 is false and Statement 2 cannot be determined
  8. Neither statement can be determined without further information
  9. True, False
  10. Statement 2 is true and Statement 1 cannot be determined

src

ori_mmlu-abstract_algebra

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Source and history

upstream_id / Original problem ID
8540
task_id
2ccbf849-d5c1-558b-8bfe-0c0315f0b97d
task_key
default--test--8540
task_revision_id
1
config / split
default / test

Official source

initial import