Relation Maths Question

Question

Prove that the relation ℝ ={(a,b) | a divides b} {Z}^+ is not an equivalence relation. ( 4 marks )

Answer 1

An equivalence relation needs to be symmetric. That is aRb => bRa.

Counterexample: (1,2) is true because 1 divides 2, however (2,1) is false because 2 does not divide 1. Therefore, (a,b) is not an equivalence relation