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.

Without using a different notation, we can substitute (a#b) for the old a and a for the old b:

((a#b)#a)#(a#b) = a

Now, replacing the (a#b)#a within this expression with b, as we are still entitled to do, we get

b#(a#b)=a

Now, renaming b as a and a as b:

a#(b#a)=b

Posted by Charlie on 2003-10-17 15:07:18