Number of relations from set A to set B

Formula for finding number of relations is

Number of relations = 2 ^{Number of elements of A × Number of elements of B}

Where does it come from?

We know that

Relation is a subset of Cartesian product A × B

Number of relations = Number of subsets of A × B

Using Formula,
Number of subsets  = 2 ^{Number of elements of set}

            = 2 ^{Number of elements of A × B}

Now,

We know that

Number of elements of A × B

   = Number of elements of A × Number of elements of B

Thus,

Number of relations = 2 ^{Number of elements of A × B}

  = 2 ^{Number of elements of A × Number of elements of B}