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.

I didn't post when this came out, but I will post now.

Start with (a#b)#a=b
Plug in (a#b) for a and a for b to give ((a#b)#a)#(a#b)=a
Substitute (a#b)#a=b on the left: b#(a#b)=a

This is what we wanted (with different letters)

Posted by Gamer on 2010-08-26 01:01:23