Consider a binary operation # that is closed under the set of integers (if a and b are integers, then a#b is an integer).

Assume that, for all integers a and b, it is true that (a#b)#a=b.

Prove that a#(b#a)=b.

(In reply to re(7): A simple solution by DJ)

I beg to differ. I showed that a#(b#a)=b (which is what the problem asks us to prove).

This is related to, but not equivalent to, that property of inverses. That I invoked that property, which I found useful in the solution is appropriate.

Posted by SilverKnight on 2003-10-20 12:33:51