How to find all relations of a set and determine which of them aren't functions? Given the following question:
"How many relations are there on {2, 3}, that aren't functions from {2, 3} to {2, 3}?"
The answer gives 16 relations, of which 12 aren't functions.
How did they conclude that? 

If $f:\{2,3\}\to \{2,3\}$ is a function then $f(2)$ can equal $2$ or $3.$ For each choice of $f(2)$ there are $2$ choices for $f(3).$ Thus $2x2=4$ functions.There are $16$ subsets of $A=\{2,3\}\times \{2,3\}.$ Subsets of $A$ are what binary relations on $\{2,3\}$ are. 
