How many functions, injections, surjections, bijections and relations from A to B are there, when A = {a, b, c}, B = {0, 1}?
Edit: I know the answer should be 64, but I don't know how to arrive at that.
I have no idea what you mean by 64.
There are $\displaystyle 2^3$ functions $\displaystyle A\to B.$
There are no injections $\displaystyle A\to B$.
Therefore, no bijections.
There are 6 surjections.
Because $\displaystyle \|A\times B\|=6$ there are $\displaystyle 2^6$ relations from $\displaystyle A\to B$ is you allow the empty relation,