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

Question

Dr. Abubacker · Accepted Answer

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

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

Explanation

Reviewed by Dr. Abubacker

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