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(5): A simple solution by DJ)
The problem DOES say thet G(F(x)) = x (for all x). Alternatively, the problem says that if F(x) = a#b, then there *is* an inverse to this relation.
That F(G(x)) = x as well... is not given by the problem, but is given by the definition of inverse relations. (That you limit the domain to the set of integers makes this no less true.)
And the fact that G is the inverse of F implies F is the inverse of G as well.
I refer you to:
http://www.math.csusb.edu/notes/func/node3.html
Edited on October 20, 2003, 4:29 am
re(6): A simple solution
