Question

Let A = {1, 2, 3, … 9} and R be the relation in A x A defined by (a, b) R (c, d). If a + d = b + c for a, b, c, d ∈ A, prove that R is an equivalence relation. Also obtain the equivalence class (2, 5).

Answer 1

Prove reflexive, prove symmetric and prove transitive 

R is reflexive, symmetric and transitive, so 

R is an equivalence relation. 

Equivalence class (2, 5) is (p, q) ⇒ 2 + q = 5 + p 

So (1, 4), (2, 5), (3, 6), (4, 7), (5, 8), (6, 9)