Question

Let $A=\{1,2,3,4\}$, $B=\{2,4,6\}$. Then the number of sets $C$ such that $A\cap B\subseteq C\subseteq A\cup B$ is

• A. $6$
• B. $9$
• C. $8$
• D. $10$

Answer 1

Answer: (C)

$A\cap B\subseteq C\subseteq A\cup B$
$\Rightarrow \left\{2,4\right\}\subseteq C\subseteq \left\{1,2,3,4,6\right\}$
Required number of sets is $8$
i.e. $\left\{2,4\right\}$, $\left\{1,2,4\right\}$, $\left\{2,4,3\right\}$, $\left\{2,4,6\right\}$, $\left\{1,2,4,3\right\}$,
$\left\{3,2,4,6\right\}$, $\left\{2,4,1,6\right\}$, $\left\{1,2,3,4,6\right\}$