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

The correct option is C $8$

$A=\{1,2,3,4\},B=\{2,4,6\}$

$A\cap B=\{2,4\}A\cup B=\{1,2,3,4,6\}$

$A\cap B\subseteq C\subseteq A\cup B\Rightarrow C=\{2,4,D\}$ where $D$ is subsets of $\{1,3,6\}$

$\Rightarrow$ No.of sets $C$= no.of subsets of $\{1,3,6\}=8$