Which of the following 5 sentences are true?

a) It is not the case that 2 consecutive sentences are both false.
b) There are fewer false than true sentences.
c) It is not the case that 3 consecutive sentences are all false.
d) It is not the case that 2 consecutive sentences are both true.
e) There are exactly 3 false sentences.

Suppose E is true. If D was true, then it would be contradictory. Thus, D would be false, so there are two consecutive true statements. This implies B must be true, and C also is true... but that makes E false. Conclusion: E is false.

Suppose D is also false; this makes A false. Since there are two consecutive true statements, B and C must be true... but this makes E true. Conclusion: D is true.

Since D is true, C must be false, and that implies A and B must also be false.

Edited on October 12, 2004, 6:39 pm

Posted by Federico Kereki on 2004-10-12 18:37:34