Let $$A = \left\{ {1,\,2} \right\},\,B = \left\{ {3,\,4} \right\}.$$      Then, number of subsets of $$A \times B$$  is :

Solution :
$$\eqalign{ & n\left( A \right) = 2{\text{ and }}n\left( B \right) = 2 \cr & n\left( {A \times B} \right) = n\left( A \right) \times n\left( B \right) = 2 \times 2 = 4 \cr & \therefore \,{\text{Number of subsets of }}A \times B = {2^{n\left( {A \times B} \right)}} = {2^4} = 16 \cr} $$