Solved: Discrete Functions: One-to-One, Onto Properties

[intervade]

Homework Statement

Suppose A, B, C are sets and [URL]http://latex.codecogs.com/gif.latex?f:A\to%20B,%20\text{%20and,%20}%20g:B\to%20C[/URL]

If f and g are one-to-one so is [PLAIN]http://latex.codecogs.com/gif.latex?g\circ%20f .[/URL]

If f and g are onto, so is [URL]http://latex.codecogs.com/gif.latex?g\circ%20f[/URL]

Homework Equations

One-to-one: [URL]http://latex.codecogs.com/gif.latex?(x,b),(y,b)\epsilon%20f%20\text{%20we%20must%20have%20}%20x=y[/URL]

Onto: Let [URL]http://latex.codecogs.com/gif.latex?f:A\to%20B,[/URL] we say f is onto B provided for every [URL]http://latex.codecogs.com/gif.latex?b\epsilon%20B[/URL] there is an [URL]http://latex.codecogs.com/gif.latex?a\epsilon%20A[/URL] so that [URL]http://latex.codecogs.com/gif.latex?f(a)=b[/URL]

The Attempt at a Solution

So.. I'm sort of lost, I've had this problem in the past, and did not understand it at all, and now its come back to haunt me. I know that:

[URL]http://latex.codecogs.com/gif.latex?im%20f%20=%20B[/URL]
[URL]http://latex.codecogs.com/gif.latex?dom%20f%20=%20A[/URL]
[URL]http://latex.codecogs.com/gif.latex?im%20g%20=%20C[/URL]
[URL]http://latex.codecogs.com/gif.latex?dom%20g%20=%20B[/URL]

But from there I'm sort of lost. Help would be much appreciated!

 

[tt2348]

Start with g(f(x))=g(f(y)), and show x=y.

 

[tt2348]

Call fx=a, fy=b , since g is one to one, what can you can about g(a)=g(b)