Question

The binary relation U = Φ (empty set) on a set A = {11, 23, 35} is _____

(a) Neither reflexive nor symmetric

(b) Symmetric and reflexive

(c) Transitive and reflexive

(d) Transitive and symmetric

I have been asked this question during an interview.

This key question is from Closure on Relations topic in portion Relations of Discrete Mathematics

Answer 1

The correct option is (d) Transitive and symmetric

To explain: U = Φ (empty set) on a set A = {11, 23, 35} need to be hold Irreflexive, symmetric, anti-symmetric, asymmetric and transitive closure property, but it is not Reflexive as it does not contain any self loop in itself.