Discrete Mathematics theory problem

1. Feb 9, 2010

CalculusSandwich

1. The problem statement, all variables and given/known data

I'm supposed to prove the following. I assume it means that (w,v) and (v,w) don't both belong to f. If they do, then f certainly isn't a single function. For instance take f= x^2. The point (2,4) certainly belongs to f, but the point (4,2) does not. It in fact belongs to f(-1). If it implies g is a set to which both (w,v) and (v,w) belong then g must contain f and it's inverse.

Problem:
Suppose f is a reversible function. The set g to which x belongs only in case x is an ordered element pair (v,w) and (w,v) belongs to f, is a function.

2. Relevant equations

A function f is reversible provided there are not two members of f having the same second term, a function f is said to be a function from its initial set onto its final set and from it's initial set to or into each of the which the final set is a subset.

3. The attempt at a solution

Inverse function relationship.
Let f and G be two functions. if G is the inverse of f then f is the inverse of G. That is, the domain of f maps the range of G and the domain of G maps the range of f.

Solution:
if f is a reversible function there exists a inverse function G, which maps f back to x for all values of x in the domain of f. Therefore the set g to which x belongs only in the case x is an ordered element pair in the terms (v,w) is the set of all ordered pairs in G. If this is the case then (w,v) belongs to f, which is a function, by the definition of inverse function relationship.