Counting functions

How many functions possible? #

If |A|=x and |B|=y, the number of functions f:A→B = $y^x$ Every element of A must be mapped to some element (amongst #y) in B

How many relations which are not functions? #

If |A|=x and |B|=y, Number of relations-Number of functions $=2^{xy}-y^x$ are the # of relations there are, which aren’t functions.