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. 

Posted by Steve Herman on 2013-07-01 19:54:06