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. $10$
• E. $12$

Answer 1

Answer: (C)

$A\cap B=\{2,4\}$ $\{A\cap B\}\subseteq \{1,2,4\},\{3,2,4\},$ $\{6,2,4\},\{1,3,2,4\}$ $\{1,3,6,2,4\}\subseteq A\cup B$ $\Rightarrow$ $n(C)=8$