Question

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 $(\mathrm{A}\cup \mathrm{C})\cap \mathrm{B}$ is?

Answer 1

Find the required set by writing list form of sets:

It is given, that

$\mathrm{A}$ is the set of the divisors of the number $15$, that is

$\mathrm{A}=\{1,3,5,15\}$

$\mathrm{B}$ is the set of prime numbers smaller than $10$, that is

$\mathrm{B}=\{2,3,5,7\}$

$\mathrm{C}$ is the set of even numbers smaller than $9$, that is

$\mathrm{C}=\{2,4,6,8\}$

Now,

$$\begin{gathered} (\mathrm{A}\cup \mathrm{C})=\{1,3,5,15\}\cup \{2,4,6,8\} \\ \Rightarrow (\mathrm{A}\cup \mathrm{C})=\{1,2,3,4,5,6,8,15\} \\ \Rightarrow (\mathrm{A}\cup \mathrm{C})\cap \mathrm{B}=\{1,2,3,4,5,6,8,15\}\cap \{2,3,5,7\} \\ \Rightarrow (\mathrm{A}\cup \mathrm{C})\cap \mathrm{B}=\{2,3,5\} \end{gathered}$$

Hence, $(\mathrm{A}\cup \mathrm{C})\cap \mathrm{B}=\{2,3,5\}$