Question

A is a non-empty set having n elements. P and Q are two subsets of A, such that P is a subset of Q. Find the number of ways of choosing the subsets P and Q.

• A. $4^n$
• B. $3^n$
• C. $2^n$
• D. $n^2$

Answer 1

The correct option is A $4^n$

${}_n\left(A\right)=n$

$P$ and $Q$ are subsets of $A$

Subsets of $A\Rightarrow$ elements in power set of $A=2^n=Q$

No of elements in power sets of $Q=2^n\left(2^n\right)=4^n$=no. of $P$