# Relation

Relation : Let A and B be two sets. Then a relation R from set A to set B is a subset of A X B. Thus, R is a relation from A to B $\Leftrightarrow $ R $ \subseteq $ A X B.Relation is generally represented by a mapping diagram and graph.

If A and B are finite sets consisting of m and n elements respectively, then A X B has 'mn' ordered pairs. So the total number of relations from A to B is 2$^{mn}$

## Example on Relation

**Example :1**Let A = {1,2,3} and B = {a,b} then total number of relations in A X B is

Number of elements in set A =3

Number of elements in set B = 2

∴ total number of relations in A X B = 2$^{3x2}$ = 2$^{6}$

A x B = {(1,a)(1,b),(2,a),(2,b),(3,a),(3,b)}

**Example 2:**The mapping diagram of the relation {(1, 2), (3, 6), (4, 10)} is shown below.

Input is the x-coordinate and output is the y-coordinate.

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