1. Tardigrade
  2. Question
  3. Mathematics
  4. Let A = 1, 2, 3, 4 B = 2, 4, 6 . Then the number of sets C such that A ∩ B ⊆ C ⊆ A ∪ B is

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Q. 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

Sets

Solution:

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