Just to reiterate, we are given that (for any integers a and b):
(a#b)#a=b,
and we have to prove that:
a#(b#a)=b.
The first thing to realize is that a and b are merely arbitrary representations of any integer.
Thus, we can rewrite the original assumption as:
(c#b)#c=b
Where c is any integer.
Then, if we replace c with b#a (which is possible because # is closed for integers):
((b#a)#b)#(b#a)=b
Then, also from the original assumption, (b#a)#b=a.
Thus, this last equation can be rewritten as:
a#(b#a)=b
Which is what we were trying to prove. |
