Question

If $n(A) = 2$ and total number of possible relations from Set $A$ to set $B$ is $1024$, then $n(B)$ is

• A. 512
• B. 20
• C. 10
• D. 5

Answer 1

Answer: (D)

5

Answer 2

Since the total number of possible relations from set A to B is 1024, each element in set A can be related to any of the elements in set B, i.e., each element in set A has n(B) possible choices for its image in set B.
Thus, the total number of possible relations from set A to B can be computed as the product of the number of choices for each element in set A, i.e.,
$n(A)=2$
Given, $2^{(n(A) \cdot n(B))}=1024$
$\Rightarrow(2)^{(2 \cdot n(B))}=(2)^{10}$
$\Rightarrow 2 \cdot n(B)=10$
$\Rightarrow n(B)=5$