relation|function,asymmetric relation,domain


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.

12th grade math


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