# Quick relations question.

1. Oct 20, 2013

### ktheo

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

True or False: Given that A = {a,b,c} and B={0,1,2,3,4}, there are 32768 binary relations from A to B

I assume there is some simple way to tell how many relations there are given two different sets, but I don't know it. Factorials? Powers? I'm not sure what.

2. Oct 20, 2013

### pasmith

A "binary relation from A to B" is formally a subset of $A \times B$, so the number of such relations is the number of subsets of $A \times B$.

3. Oct 20, 2013

### Dick

Try and work it out. How many total ordered pairs are there in AxB? Now each ordered pair can either be in the relation or not.