Question

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

• A. $2$
• B. $4$
• C. $8$
• D. $10$

Answer 1

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.