Similarly, (a, b) ∈ R1 ∩ R2 and
(b, c) ∈ R1 ∩ R2 ⇒ (a, c) ∈ R1 and (a, c) ∈ R2 ⇒ (a, c) ∈ R1 ∩ R2 This shows that
R1 ∩ R2 is transitive Thus, R1 ∩ R2 is an equivalence relation Example 19 Let R be a relation on the set A of ordered pairs of positive integers
defined by (x, y) R (u, v) if  and only if xv = yu