Consider these four statements. S1: S2, S3 and S4 are all true. S2: Exactly two of these four statements are true. S3: S1 is false. S4: S2 and S3 have the same truth value. Which of the statements are true?
Answer and explanation
Correct answer: A. Only statement 3 is true
- Step 1: Try S1 true: then S2, S3, S4 are all true, but S3 says S1 is false. Contradiction, so S1 is false and S3 is true.
- Step 2: If S2 were true there would need to be exactly two true statements, with S3 one of them; then S4 ('S2 and S3 same') would be true, making three. So S2 is false, and then S4 is false (S2 false, S3 true differ). Only S3 is true.
Answer
Only statement 3 is true.
Why not the others: Any assignment with S1 true contradicts S3; adding S2 or S4 to S3 changes the count and breaks the claim of S2 or S4.
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