Revision Notes
Class-12 Mathematics
Chapter 1 – Relations and Functions
Relation
● It defines relationship between two set of values let say from set A to
set B.
● Set A is then called domain and set B is then called codomain.
● If a, b R , it shows that a is related to b under the relation R
Types of Relations
1. Empty Relation:
● In this there is no relation between any element of a set.
● It is also known as void relation
● For example: if set A is 2, 4, 6 then an empty relation can be R x, y
where x y 11
2. Universal Relation:
● In this each element of a set is related to every element of that set.
● For example: if set A is 2, 4, 6 then a universal relation can be
R x, y where x y 0
3. Trivial Relation: Empty relation and universal relation is sometimes
called trivial relation.
4. Reflexive Relation:
● In this each element of set (say) A is related to itself i.e., a relation R in
set A is called reflexive if a,a R for every a A .
● For example: if Set A 1, 2,3 then relation
R 1,1,1, 2 , 2, 2,2,1,3,3 is reflexive since each element of set
A is related to itself.
Class XII Mathematics www.vedantu.com 1
Class-12 Mathematics
Chapter 1 – Relations and Functions
Relation
● It defines relationship between two set of values let say from set A to
set B.
● Set A is then called domain and set B is then called codomain.
● If a, b R , it shows that a is related to b under the relation R
Types of Relations
1. Empty Relation:
● In this there is no relation between any element of a set.
● It is also known as void relation
● For example: if set A is 2, 4, 6 then an empty relation can be R x, y
where x y 11
2. Universal Relation:
● In this each element of a set is related to every element of that set.
● For example: if set A is 2, 4, 6 then a universal relation can be
R x, y where x y 0
3. Trivial Relation: Empty relation and universal relation is sometimes
called trivial relation.
4. Reflexive Relation:
● In this each element of set (say) A is related to itself i.e., a relation R in
set A is called reflexive if a,a R for every a A .
● For example: if Set A 1, 2,3 then relation
R 1,1,1, 2 , 2, 2,2,1,3,3 is reflexive since each element of set
A is related to itself.
Class XII Mathematics www.vedantu.com 1
