\[\begin{align}  & (X\cap Y)'=X'\cup Y' \\ & \text{From the L}\text{.H}\text{.S} \\ & \text{Let }a\in (X\cap Y)' \\ & a\notin X\cap Y \\ & a\notin X\text{ or }a\notin Y \\ & a\in X'\text{ or }a\in Y' \\ & a\in X'\cup Y' \\ & X'\cup Y'\subseteq (X\cap Y)' \\ & \text{From R}\text{.H}\text{.S} \\ & \text{Let }b\in X'\cup Y' \\ & b\in X'\text{ or }b\in Y' \\ & b\notin X\text{ and }b\notin Y \\ & b\notin X\cap Y \\ & b\in (X\cap Y)' \\ & (X\cap Y)'\subseteq X'\cup Y'----(ii) \\ & \therefore (X\cap Y)'=X'\cup Y' \\\end{align}\]