Question

If $A=\{1,2,3,4\}$ & $B=\{2,4,6\}$. Then, the number of set ‘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

$8$

Explanation for the correct option:

Finding number of set:

Given,

$\begin{array}{rcl}A& =& \hspace{0.17em}\{1,2,3,4\}\\ B& =& \{2,4,6\}\end{array}$

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

Now,

$$\begin{gathered} A\cap B\subseteq C\subseteq A\cup B \\ \{1,2\}\subseteq C\subseteq \{1,2,3,4,6\} \\ C=\{2,4\},\{1,2,3,4,6\},\{2,4,1\},\{2,4,3\},\{2,4,6\},\{2,4,1,3\},\{2,4,1,6\},\{2,4,3,6\} \end{gathered}$$

Number of set $=8$

Hence, correct answer is (C)