# What is the number of relations on a set?

Hint: In order to solve this problem you dont need to count the number of relations by assuming it on your own. You have to use the formula of the number of relations from set A to

Hint: In order to solve this problem you dont need to count the number of relations by assuming it on your own. You have to use the formula of the number of relations from set A to set B. Doing this will solve your problem.

$\Rightarrow {2^{{\text{(number of elements in first set) }} \times {\text{ (number of elements in second set)}}}}$
$\Rightarrow {2^{{\text{n(A)}} \times {\text{n(B)}}}} \\ \Rightarrow {2^{2 \times 2}} = {2^4} = 2 \times 2 \times 2 \times 2 \\ \Rightarrow 16 \\$
Note: To solve such problems of sets we need to use the formula of the number of relations from one set to another can be written as ${2^{{\text{(number of elements in first set) }} \times {\text{ (number of elements in second set)}}}}$. By just knowing this formula you will get the right answer. Students usually try to count the number of relations by themselves doing this can give you wrong answers generally.