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Hi guys I was wondering if someone could give me a little cheat sheet for my quiz tomorrow to help pick up on relations. Can't seem to find my discrete mathematics book

This is what I need to know:

Define a relation R from {...} to {...} by R = {(..., ...), (..., ...), (..., ...), (..., ...)}.

The source of R

The Domain of R

The target or co-domain of R is

The range of R is

The inverse of R is

A website link would be fine that explains these nicely. Greatly appreciate any help.

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Have you looked at en.wikipedia.org/wiki/Binary_relation? –  LostInMath Oct 5 '11 at 13:04
    
Yeah that's helped a bit. Still going through it but it seems a few things I need to know aren't there. –  poipoi1 Oct 5 '11 at 13:06
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1 Answer 1

up vote 2 down vote accepted

Summary of the wikipedia-entry according to your questions:

A relation is a triple $(X,Y,G)$, where $X,Y$ are sets and $G$ is a subset of the cartesian product $X\times Y$.

In this case $X$ is called the domain and $Y$ is called the codomain.

If $(X,Y,G)$ is a relation, then the inverse is defined as $(Y,X,G^{-1})$, where $G^{-1}=\{(y,x)|(x,y)\in G\}$.

Range has different meanings, for you it is probably $\{y\in Y|\exists x\in X: (x,y)\in G\}$.

I didn't find a definition of source, it could be the dual thing to range, that would make most sense in your list. How is it used in your book?

Here is a further hyperlink that I found via google: Proofwiki

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wow perfect! thanks! –  poipoi1 Oct 5 '11 at 13:55
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