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.