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If $\mathrm{A}$ is the set of the divisors of the number $15, \mathrm{~B}$ is the set of prime numbers smaller than 10 and $\mathrm{C}$ is the set of even numbers smaller than 9 , then find the set representing $(A \cup C) \cap B$.
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Verified Answer
$$
\begin{aligned}
&\mathrm{A}=\{1,3,5,15\}, \mathrm{B}=\{2,3,5,7\} \mathrm{C}=\{2,4,6,8\} \\
&\therefore \mathrm{A} \cup \mathrm{C}=\{1,2,3,4,5,6,8,15\} \\
&(\mathrm{A} \cup \mathrm{C}) \cap \mathrm{B}=\{2,3,5\}
\end{aligned}
$$
\begin{aligned}
&\mathrm{A}=\{1,3,5,15\}, \mathrm{B}=\{2,3,5,7\} \mathrm{C}=\{2,4,6,8\} \\
&\therefore \mathrm{A} \cup \mathrm{C}=\{1,2,3,4,5,6,8,15\} \\
&(\mathrm{A} \cup \mathrm{C}) \cap \mathrm{B}=\{2,3,5\}
\end{aligned}
$$
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