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