Class 12 Maths

Relation and Function

NCERT Solution

Exercise 1.1 Part 1

Question 1: Determine whether each of the following relations are reflexive, symmetric and transitive.

(i) Relation R in the set A = {1, 2, 3, ..........., 13, 14} defined as Solution: Thus, R is not reflexive Thus, R is not symmetric Therefore, R is not transitive

Thus, R is neither reflexive nor symmetric and nor transitive.

(ii) Relation of R in the set N of natural numbers defined as Solution: Thus, R is not reflexive relation Thus, R is not symmetric Thus, R is not transitive.

Therefore, R is neither Reflexive, nor symmetric and nor transitive.

(iii) Relation R in the set A = {1, 2, 3, 4, 5, 6} Solution: Given,R={(x,y):y is divisible by x} in A={1,2,3,4,5,6}

Here, R = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 2), (2, 4), (2, 6), (3,3), (3, 6), (4,4), 5, 5), (6, 6)} Thus, R is reflexive. Thus, R is not symmetric. Thus, R is transitive.

Therefore, R is reflexive and transitive but not symmetric.

(iv) Relation R in the set Z of all integers defined as Solution: In set Z of all integer. Therefore, R is reflexive relation. Therefore, R is symmetric. Therefore, R is transitive.

Thus, R is reflexive, symmetric and transitive.

Exercise 1

Exemplar Problems