There is a club called the Exclusive Club. Somebody is a member of this club if and only if he has not shaved anybody who has shaved him. In other words, X is a member of the Exclusive Club if and only if there is no Y such that X shaves Y and Y shaves X.
A barber once claimed that he had shaved every member of the Exclusive Club and nobody else. Show that the barber's claim cannot be true.
(In reply to re: solution
by Ady TZIDON)
I rise to Daniels' defense. The problem is quite clear that somebody is a member of this club if he has not shaved anybody who has shaved him. If you meet the requirements, then you are a member.
It's sort of like being a member of the human race. If you are human, then you're a member.