Let set $R = {P : B \subseteq P \subseteq A} .$ If $A = {1, 2, 3, 4, 5}$ and $B = {1, 2},$ then the number of elements in set $R$ is

2

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4

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8

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10

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Solution

The correct option is C $8$
Since $P$ is superset of $B$ so $P$ contains ${1, 2}$ .
Now for subset of $A$ , $P$ has all possible combinations of ${3, 4, 5}$ as a set.
Number of subsets of ${3, 4, 5}$
$= 2^{3}$
$= 8$ elements.

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