Question: Suppose a set A has n elements and a set B has m elements. Prove that there are 2^m*n different relations from A to B
Now i see how this works with the product rule with AXB with m*n elements. and there are two sets so thats where 2 is involved. So i guess all the pieces are there but i don't know what to do with them.
If S is a set, the number of subsets of S is .
Here is a brief outline of a proof.
If we form the set of bit-strings, strings of 0's & 1's, of length n, then that set has elements.
If then the string represents the subset . So every 4-bit-string represents a subset of so there are subsets of .