Let R and S be two non-void relations on a set A. Which of …

Maths Set Theory and Relations Relations Single Correct MCQ

Published by: CGP EDU Academic Team

Published on: August 14, 2026

Let R and S be two non-void relations on a set A. Which of the following statements is false

R and S are transitive ⇒ ⇒ R ∪ ∪ S is transitive

R and S are transitive ⇒ ⇒ R ∩ ∩ S is transitive

R and S are symmetric ⇒ ⇒ R ∪ ∪ S is symmetric

R and S are reflexive ⇒ ⇒ R ∩ ∩ S is reflexive

Text Solution

Verified by Experts

The correct answer is:

Let and R = {(1, 1), (1, 2)}, S = {(2, 2) (2, 3)} be transitive relations on A.

Then R ∪ ∪ S = {(1, 1); (1, 2); (2, 2); (2, 3)}

Obviously, R ∪ ∪ S is not transitive. Since (1, 2) R ∪ ∪ S and but (1, 3) .

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