Question

Determine the characteristics of the relation aRb if a^2 = b^2.

(a) Transitive and symmetric

(b) Reflexive and asymmetry

(c) Trichotomy, antisymmetry, and irreflexive

(d) Symmetric, Reflexive, and transitive

I had been asked this question in an interview for job.

This interesting question is from Types of Relations in section Relations of Discrete Mathematics

Answer 1

Right answer is (d) Symmetric, Reflexive, and transitive

The best I can explain: Since, x^2 = y^2 is just a special case of equality, so all properties that apply to x = y also apply to this case. Hence, the relation satisfies symmetric, reflexive and transitive closure.