Consider these three statements. S1: Exactly one of S2 and S3 is true. S2: Exactly one of S1 and S3 is true. S3: Neither S1 nor S2 is true. Which of the statements are true?
Answer and explanation
Correct answer: A. Statements 1 and 2 are true
- Step 1: Suppose S3 is true. Then S1 and S2 are false. But S1 ('exactly one of S2, S3 is true') would then be true, since S3 is true and S2 false. Contradiction. So S3 is false.
- Step 2: With S3 false, S1 says 'exactly one of S2, S3 is true', which holds if and only if S2 is true; similarly S2 holds iff S1 is true. So S1 and S2 are both true (and both claims check out since S3 is false).
Answer
Statements 1 and 2 are true.
Why not the others: Making S3 true contradicts itself; making only one of S1, S2 true breaks the other's claim.
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