Consider these three statements. S1: S2 and S3 are both false. S2: S1 is true or S3 is true. S3: Exactly one of S1 and S2 is true. Which of the statements are true?
Answer and explanation
Correct answer: D. Statements 2 and 3 are true
- Step 1: If S1 were true, S2 and S3 would both be false. But S2 says 'S1 is true or S3 is true' and S1 is true, so S2 would be true. Contradiction. So S1 is false.
- Step 2: With S1 false, S3 ('exactly one of S1, S2 is true') requires S2 true; then S3 is true, and S2's claim ('S1 or S3') holds because S3 is true. So S2 and S3 are true and S1 is false, which is consistent.
Answer
Statements 2 and 3 are true.
Why not the others: Any assignment making S1 true fails because S1 would then be contradicted by S2's claim; S1 alone or all three fail for the same reason.
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