Which of the following is correct ?
I. $$n\left( {S \cup T} \right)$$   is maximum when $$n\left( {S \cap T} \right)$$   is least.
II. If $$n\left( U \right) = 1000,\,n\left( S \right) = 720,\,n\left( T \right) = 450,$$        then least value of $$n\left( {S \cap T} \right) = 170$$

Solution :
Both the statements are true.
$$\eqalign{ & {\text{II}}{\text{. }}n\left( {S \cup T} \right) = n\left( S \right) + n\left( T \right) - n\left( {S \cap T} \right) \cr & = 720 + 450 - n\left( {S \cap T} \right) \cr & = 1170 - n\left( {S \cap T} \right) \cr & \Rightarrow 1170 - n\left( {S \cap T} \right) \leqslant n\left( U \right) \cr & \Rightarrow 1170 - n\left( {S \cap T} \right) \leqslant 1000 \cr & \Rightarrow n\left( {S \cap T} \right) \geqslant 170 \cr} $$