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

Question 1: (i)Relation R in the set A = {1, 2, 3…13, 14} defined as R = {(x, y): 3x − y = 0}

Solution:- (i) A = {1, 2, 3 … 13, 14}

R = {(x, y): 3x − y = 0}

∴R = {(1, 3), (2, 6), (3, 9), (4, 12)}

R is not reflexive since (1, 1), (2, 2) … (14, 14) ∉ R.

Also, R is not symmetric as (1, 3) ∈R, but (3, 1) ∉ R. [3(3) − 1 ≠ 0]

Also, R is not transitive as (1, 3), (3, 9) ∈R, but (1, 9) ∉ R.

[3(1) − 9 ≠ 0]

Hence, R is neither reflexive, nor symmetric, nor transitive.

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How Many Questions are there in Class 12 Maths NCERT Solutions Chapter 1 Relations and Functions?

NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions has 55 questions in 4 exercises. The practice of these exercises is useful For Self Study.