Consider these three statements. S1: At least one of S2 and S3 is false. S2: S1 is true. S3: S1 and S2 are both false. Which of the statements are true?
Answer and explanation
Correct answer: E. Statements 1 and 2 are true
- Step 1: Suppose S1 is false. Then S2 ('S1 is true') is false, and S3 ('S1 and S2 are both false') is true. But S1 says 'at least one of S2 and S3 is false', and S2 is false, so S1's claim would be correct and S1 would be true. That is a contradiction, so S1 is true.
- Step 2: Since S1 is true, S2 is true. Then S3 ('both false') is false, which makes S1's claim ('at least one of S2, S3 is false') correct. This is consistent: S1 and S2 are true, S3 is false.
Answer
Statements 1 and 2 are true.
Why not the others: Each other combination breaks at least one statement's own claim: for example if only S1 were true, S2 would be false while S1 is true, contradicting S2's claim.
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