The relation R is defined in the set {1, 2, 3, 4, 5, 6} as …

Maths Set Theory and Relations NTA Abhyas Questions Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 13, 2026

The relation R is defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b): b = a + 1}, then

R is neither reflexive nor symmetric nor transitive

R is neither reflexive nor symmetric but transitive

R is not reflexive but symmetric and transitive

R is reflexive, symmetric and transitive

Text Solution

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The correct answer is:

R is neither reflexive nor symmetric nor transitive

Let, A = {l, 2, 3, 4, 5, 6}

The relation R is defined on set A is

R = {(a, b): b = a + 1}. Therefore, R = {(1, 2), (2, 3), (3, 4), (4, 5), (5, 6)}

Now, 6 A but (6, 6) R.

Therefore, R is not reflexive.

It can be observed that (1, 2) R but (2,1) R. Therefore, R is not symmetric.

Now, (1, 2), (2, 3) R but (l, 3) R Therefore, R is not transitive.

Hence, R is neither reflexive nor symmetric nor transitive

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