3
$\begingroup$

A question has appeared in our Informatics Olympiad which there is a lot of discussion over it. the problem states:

Below are 5 statements. At most how many of them can be true together?

a) if b is true then this statement is false.

b) if number of the true statements is greater than $2$, then one of them is c.

c) at least one of a and d is false.

d) b and c are both true or both false.

e) b is true or false.

many say this number is $3$, by statements a,d,e being true and the rest false, and many other say this number is $4$, a being false and the rest being true. what is your opinion? which group say the truth?

EDIT. I made a mistake and typed ''wrong'' in statement c instead of ''false''. now it's correct.

  • 0
    If **b** is true and **a** is false, then **a** is true; you cannot have **a** false and **b** true, so "many other" is wrong.2012-02-27
  • 0
    statement a is self-refential. Normaly in propositional logic you do not admit self-reference because it leads to antinomies.2012-02-27
  • 0
    when and where will it be possible to see the official answer to this question?2012-02-27
  • 0
    @magma: I doubt if there will be any official solution, since it appeared in a multiple choice exam, but if there was one, I'll inform you.2012-02-27

2 Answers 2