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.

if a is true, then b can be either true or false.  if b is false, then e must be true. if these are both correct then d can be neither true nor false because if it is true, then it is contradicting itself with d and e being true. d could be false, which means that c must be either true or false. if c is true, then it disproves e and b which are hypothetically true and false respectively. if c is false, then everything is correct except that if c is false then a must be false, and a is true.  so a cannot be true.

if a is false, then again b can be either true or false.  if be is false, then e must be true (again).  so then you look at d. if it is false, then two consecutive sentences must be true, which can't be true because it is ff_ft.  if d is true, then it is disproving itself because e is true.  so you go back to b, which must be true, because it cannot be false; which means that e must be false.  if d is false, then c must be true or false.  given d, c must be true, but this disproves both b and d.  if d is true, then c must be false given d, which disproves b and e.   

Posted by aria on 2004-10-25 03:42:04