$\begin{align} & \text{Let }A=\{a,b,c,d,e\},\text{ }B=\{a,d,e,f,g\}\text{ and } \\ & C=\{a,c,ef,g\} \\ & \text{compute} \\ & (a)\text{ }A\cap B \\ & (b)A\cap C \\ & (c)B\cap C \\ & (d)A\cup B \\ & (e)A\cup C \\ & (f)B\cup C \\ & (g)(A\cup B)\cup C \\ & (h)(A\cap B)\cap C \\ & (i)A\cap (B\cap C) \\ & (j)A\cup (B\cap C) \\\end{align}$
$\begin{align} & (a)A\cap B=\{a,b,c,d,e\}\cap \{a,d,e,f,g\}=\{\{a,d,e\} \\ & (b)A\cap C=\{a,b,c,d,e\}\cap \{a,c,e,f,h\}=\{a,c,e\} \\ & (c)B\cap C=\{a,d,e,f,g\}\cap \{a,c,e,f,h\}=\{a,e,f\} \\ & (d)A\cup B=\{a,b,c,d,e,f,g\} \\ & (e)A\cup C=\{a,b,c,d,e,f,h\} \\ & (f)B\cup C=\{a,c,d,e,f,g,h\} \\ & (g)\text{ }(A\cup B)\cup C=\{a,b,c,d,e,f,g,h\} \\ & (h)(A\cap B)\cap C=\{a,e\} \\ & (i)A\cap (B\cap C)=\{a,e\} \\ & (j)A\cup (B\cap C)=\{a,b,c,d,e,f\} \\\end{align}$