Department of Pre-University Education, KarnatakaPUC Karnataka Science Class 12
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Determine Whether the Following Relations Are Reflective, Symmetric and Transitive: Relation R in the Set a = {1, 2, 3...13, 14} Defined as R = {x,y):3x - y = 0} - Mathematics

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Determine whether  the following relations are reflective, symmetric and transitive:

Relation R in the set  A  = {1, 2, 3...13, 14} defined as R = {(x,y):3x - y = 0}

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Solution

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 (1,2), (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. 

Concept: Types of Relations
  Is there an error in this question or solution?

APPEARS IN

NCERT Class 12 Maths
Chapter 1 Relations and Functions
Q 1.1 | Page 5
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