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.

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- May 8th 2011, 08:59 AMposix_memalignNumber of functions from one set to another?
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. - May 8th 2011, 09:13 AMPlato
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, - May 8th 2011, 09:40 AMposix_memalign
- May 8th 2011, 09:46 AMPlato