Question

Let A = {1,2} and B = {3,4}. Find the number of relations from A to B.

Answer 1

Hint: In order to solve this problem you don’t 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.

Complete step-by-step answer:
 It is given that A = {1, 2} and B = {3, 4}
We know that the number of elements in A is n(A)=2 and that of B is n(B) = 2.
We also know the formula that the number of relations from one set to another can be written as:
$ \Rightarrow {2^{{\text{(number of elements in first set) }} \times {\text{ (number of elements in second set)}}}}$
On this case we can write number of relations as:
$
   \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 \\
$
Hence, the number of relations from A to B is 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.