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MMLU-Pro / 7792 / Statement 1 | For every positive integer n there is a cyclic group of order n.…

Problem

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

question

Statement 1 | For every positive integer n there is a cyclic group of order n. Statement 2 | Every finite cyclic group contains an element of every order that divides the order of the group.

category

math

options

  1. Statement 1 is false because not all positive integers have a cyclic group. Statement 2 is true.
  2. Statement 1 is false because only composite numbers have a cyclic group. Statement 2 is true.
  3. False, False
  4. True, False
  5. False, True
  6. Statement 1 is false because only prime numbers have a cyclic group. Statement 2 is true.
  7. Statement 1 is true because all positive integers have a cyclic group. Statement 2 is false because only infinite cyclic groups contain an element of every order that divides the order of the group.
  8. True, True
  9. Both statements are true, but they are not related.
  10. Statement 1 is true because all positive integers have a cyclic group. Statement 2 is false because not all finite cyclic groups contain an element of every order that divides the order of the group.

src

ori_mmlu-abstract_algebra

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Source and history

upstream_id / Original problem ID
7792
task_id
af030fa3-16a1-5bfb-9ed8-786c449e465a
task_key
default--test--7792
task_revision_id
1
config / split
default / test

Official source

initial import