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 solution by Daniel)

3)..... A non club member: then the barber meets the requirements for membership and thus must be a member, contradicting his not being a member....

Posted by Ady TZIDON on 2013-07-01 18:39:56