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(2): solution by Steve Herman)

thank you Steve.  The key part is the use of "if and only if" in the second sentence describing membership requirements.

Posted by Daniel on 2013-07-01 21:13:55