CBSE Notes Class 12 Chapter 1 – Relations and
Functions
Relations
A relation can be mathematically defined as the linking or connection between two different
objects or quantities.
Examples of relations:
(i) {(a, b) ∈ A × B: a is brother of b},
(ii) {(a, b) ∈ A × B: a is sister of b},
(iii) {(a, b) ∈ A × B: age of a is greater than age of b},
(iv) {(a, b) ∈ A × B: total marks obtained by a in the final examination is less than the
total marks obtained by b in the final examination},
(v) {(a, b) ∈ A × B: a lives in the same locality as b}. However, abstracting from this, we
define mathematically a relation R from A to B as an arbitrary subset of A × B.
Types of Relations
Empty Relation
Universal Relation
Reflexive Relation
Symmetric relation
Transitive relation
Equivalence relation
Empty Relation: A relation R in a set A is called empty relation, if no element of A is related
to any element of A, i.e., R = φ ⊂ A × A.
Universal Relation: A relation R in a set A is called universal relation, if each element of A is
related to every element of A, i.e., R = A × A.
Reflexive Relation: A relation R in a set A is said to be an equivalence relation if R is
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Functions
Relations
A relation can be mathematically defined as the linking or connection between two different
objects or quantities.
Examples of relations:
(i) {(a, b) ∈ A × B: a is brother of b},
(ii) {(a, b) ∈ A × B: a is sister of b},
(iii) {(a, b) ∈ A × B: age of a is greater than age of b},
(iv) {(a, b) ∈ A × B: total marks obtained by a in the final examination is less than the
total marks obtained by b in the final examination},
(v) {(a, b) ∈ A × B: a lives in the same locality as b}. However, abstracting from this, we
define mathematically a relation R from A to B as an arbitrary subset of A × B.
Types of Relations
Empty Relation
Universal Relation
Reflexive Relation
Symmetric relation
Transitive relation
Equivalence relation
Empty Relation: A relation R in a set A is called empty relation, if no element of A is related
to any element of A, i.e., R = φ ⊂ A × A.
Universal Relation: A relation R in a set A is called universal relation, if each element of A is
related to every element of A, i.e., R = A × A.
Reflexive Relation: A relation R in a set A is said to be an equivalence relation if R is
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