$\begin{align}  & \text{Let }\mu =\{1,2,3,\cdot \cdot \cdot ,10\},\text{ }X=\{2,4,6,8\},Y=\{1,2,3,4\}\text{ and }Z=\{3,4,5,6,8\} \\ & X'=\{1,3,5,7,9,10\},\text{ }Y'=\{5,6,7,8,9,10\} \\ &  \\ & \text{To show that }(X\cup Y)'=X'\cap Y' \\ & (X\cup Y)=\{2,4,6,8\}\cup \{1,2,3,4\}=\{1,2,3,4,6,8\} \\ & (X\cup Y)'=\{5,7,9,10\}----(i) \\ & X'=\{1,3,5,7,9,10\},\text{ }Y'=\{5,6,7,8,9,10\} \\ & X'\cap Y'=\{5,7,9,10\}----(ii) \\ & \text{Comparing }(i)\text{ and }(ii)\text{ we can conclude that} \\ & (X\cup Y)'=X'\cap Y' \\ &  \\ & \text{To show that }(Y\cap Z)'=Y'\cup Z' \\ & \mu =\{1,2,3,4,5,6,7,8,9,10\}, \\ & X=\{2,4,6,8\},Y=\{1,2,3,4\} \\ & \text{and }Z=\{3,4,5,6,8\} \\ & (Y\cap Z)=\{1,2,3,4\}\cap \{3,4,5,6,8\}=\{3,4\} \\ & (Y\cap Z)'=\{1,2,5,6,7,8,9,10\}---(i) \\ & Y'=\{5,6,7,8,9,10\},\text{ }Z'=\{1,2,7,9,10\} \\ & Y'\cup Z'=\{5,6,7,8,9,10\}\cup \{1,2,7,9,10\} \\ & Y'\cup Z'=\{1,2,5,6,7,8,9,10\}---(ii) \\ & \text{Comparing }(i)\text{ and }(ii)\text{ together, we can conclude that} \\ & \text{ }(Y\cap Z)'=Y'\cup Z' \\\end{align}$