Let R be the relation in the set {1, 2, 3.4} given by
R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}.
Choose the correct answer.
(A). R is reflexive and symmetric but not transitive.
(B). R is reflexive and transitive but not symmetric.
(C). R is symmetric and transitive but not reflexive.
(D). R is an equivalence relation.

Solution:

Given that R be the relation in the set {1, 2, 3.4} given by

R = {(1, 2)(2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}

(a, a) ∈ R for every a ∈ {1, 2, 3.4}

∴ R is reflexive.

(1, 2) ∈ R but (2, 1) ∉ R

∴ R is not symmetric.

(a, b),(b, c) ∈ R for all a, b, c ∈ {1, 2, 3, 4}

∴ R is not transitive.

R is reflexive and transitive but not symmetric.

The correct answer is B

NCERT Solutions for Class 12 Maths - Chapter 1 Exercise 1.1 Question 15

Let R be the relation in the set {1, 2, 3.4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer. (A). R is reflexive and symmetric but not transitive.(B). R is reflexive and transitive but not symmetric. (C). R is symmetric and transitive but not reflexive. (D). R is an equivalence relation.

Summary:

Given that R be the relation in the set {1, 2, 3.4} given by R = {(1, 2), (2, 2), (1, 1), (4, 4), (1, 3), (3, 3), (3, 2)}. Hence, R is reflexive and transitive but not symmetric