Question

If A = {1, 3, 5, 7, 9, 11} and B = {set of prime numbers in set A}, find the number of subsets of A n B.A. 10B. 14C.16D. 24

Answer 1

Answer:

C. 16

Explanation:

Given the sets A and B below:

• A = {1, 3, 5, 7, 9, 11}

,

• B = {set of prime numbers in set A}

The elements of B are listed below:

$B=\mleft\{3,5,7,11\mright\}$

The intersection of sets A and B is the set of elements common to both A and B.

This is given below:

$A\cap B=\{3,5,7,11\}$

If a set has n elements, the number of subsets = 2^n.

$\begin{gathered} \text{Number of elements,}n(A\cap B)=4 \\ \text{Number of subsets}=2^4=16 \end{gathered}$

The number of subsets of AnB is 16.