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MMLU-Pro / 11189 / Use indirect truth tables to determine whether the following argument is valid.…

Problem

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

question

Use indirect truth tables to determine whether the following argument is valid. If the argument is invalid, choose an option which presents a counterexample. (There may be other counterexamples as well.)
P ⊃ (Q ∨ R)
(Q · S) ⊃ ~P
~(~Q ∨ R) / ~P

category

philosophy

options

  1. Invalid. Counterexample when P, Q, R, and S are true
  2. Valid
  3. Valid. No counterexamples exist
  4. Invalid. Counterexample when P and R are true and Q and S are false
  5. Invalid. Counterexample when P is true, Q, R, and S are false
  6. Invalid. Counterexample when P and Q are true and R and S are false
  7. Invalid. Counterexample when P is false, Q, R, and S are true
  8. Invalid. Counterexample when P, R, and S are true and Q is false
  9. Invalid. Counterexample when P and S are true and Q and R are false

src

ori_mmlu-formal_logic

Discussion

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Source and history

upstream_id / Original problem ID
11189
task_id
f18e0795-5c07-578d-92d2-325db015a955
task_key
default--test--11189
task_revision_id
1
config / split
default / test

Official source

initial import