If $$n\left( A \right) = 115,\,n\left( B \right) = 326,\,n\left( {A - B} \right) = 47,$$         then what is $$n\left( {A \cup B} \right)$$   equal to ?

Solution :
We know, for two sets $$A$$ and $$B$$
$$\eqalign{ & A - B = A - \left( {A \cap B} \right) \cr & \therefore \,n\left( {A - B} \right) = n\left( A \right) - n\left( {A \cap B} \right) \cr & {\text{Given, }}n\left( A \right) = 115,\,n\left( B \right) = 326{\text{ and }}n\left( {A - B} \right) = 47 \cr & \Rightarrow \,47 = 115 - n\left( {A \cap B} \right) \cr & \Rightarrow \,n\left( {A \cap B} \right) = 68 \cr & {\text{Consider }}n\left( {A \cup B} \right) = n\left( A \right) + n\left( B \right) - n\left( {A \cap B} \right) \cr & = 115 + 326 - 68 = 373 \cr} $$