$$\eqalign{ & {\text{Let }}A = \left\{ {x\, \in \,W,{\text{ the set of whole numbers and }}x < 3} \right\} \cr & \,\,\,\,\,\,\,\,\,\,B = \left\{ {x\, \in \,N,{\text{ the set of natural numbers and }}2 \leqslant x < 4} \right\} \cr & {\text{and }}C = \left\{ {3,\,4} \right\} \cr} ,$$
then how many elements will $$\left( {A \cup B} \right) \times C$$   contain ?

Solution :
$$\eqalign{ & {\text{We have}} \cr & A = \left\{ {0,\,1,\,2} \right\} \cr & B = \left\{ {2,\,3} \right\} \cr & C = \left\{ {3,\,4} \right\} \cr & \left( {A \cup B} \right) = \left\{ {0,\,1,\,2,\,3} \right\} \cr & \left( {A \cup B} \right) \times C = \left\{ {\left( {0,\,3} \right),\,\left( {0,\,4} \right),\,\left( {1,\,3} \right);\left( {1,\,4} \right);\left( {2,\,3} \right),\,\left( {2,\,4} \right),\,\left( {3,\,3} \right);\left( {3,\,4} \right)} \right\} \cr & \therefore \,n\left[ {\left( {A \cup B} \right) \times C} \right] = 8 \cr} $$