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.

(In reply to food for thought by aria)

I deduced that the following sentences are true/false:

FFTFT, with the first being a) and last being e)

So sentences c) and e) are true

Heres how i came to the solution: I noticed that b) and e) are always going to be opposite of eachother. I then branched off both possible situations. If b) is F then e) T, and i also assumed that a) is T, this formed a contradiction. So a) must be F. Then i went assuming d) was T, which went into a contradiction. So then decuded FFTFT, ( c & e being T ). I tried the same procedure with b) T and e) F and went into a contradiction for all possibilities. 

 

 

Posted by Mike on 2004-11-22 21:00:40