Question

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

(a) A and B are transitive ⇒ A∩B is transitive

(b) A and B are symmetric ⇒ A∪B is symmetric

(c) A and B are transitive ⇒ A∪B is not transitive

(d) A and B are reflexive ⇒ A∩B is reflexive

I got this question in an online interview.

I'm obligated to ask this question of Types of Relations topic in section Relations of Discrete Mathematics

Answer 1

Correct option is (c) A and B are transitive ⇒ A∪B is not transitive

The explanation: In terms of set theory, the binary relation R defined on the set X is a transitive relation if, for all a, b, c ∈ X, if aRb and bRc, then aRc. If there are two relations on a set satisfying transitive property then there union must satisfy transitive property.