Question

Which of the following is an equivalence relation

on R, for a, b  Z ?

(a) ab  Z (b) a  c Z

2

(c) ab  cd / 2 Z (d) 2c /3 Z

3​

Answer 1

Answer:

Definition 1. An equivalence relation is a relationship on a set, generally denoted by “∼”, that is reflexive, symmetric, and transitive for everything in the set. ... Example: The relation “is equal to”, denoted “=”, is an equivalence relation on the set of real numbers since for any x, y, z ∈ R: 1.