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