1 What is an equivalence relation Is a b an equivalence rela

1) What is an equivalence relation? Is a b an equivalence relation on the set
of real numbers?

Solution

A relation R on a set S is an equivalence relation if and only if R is

(1) Reflexive

(2) Symmetric

(3) Transitive

The relation \"is less than or equal to\" () is not an equivalence relation on the set of real numbers.

thus a b is not an equivalence relation on the set of real numbers.