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.

Given (a*b)*a = b and given a*b is closed, then a*b = b*a under the commutative property of real numbers. Thus,(a*b)*a = (b*a)*a.

We can then say (b*a)*a = a*(b*a) under the commutative property. By substitution (or transitive property), (a*b)*a = a*(b*a).

Using the substitution (or transitive) property it follows that if (a*b)*a = b and (a*b)*a = a*(b*a) than a*(b*a) = b.

Posted by Angela on 2003-10-19 11:15:50