“Don’t let the fear of losing be greater than the excitement of winning.” —Robert Kiyosaki

Question 12. Let A = {1, 2, 3, …. , 12} and R be a relation in A x A defined by (p, q) R (r, s) if ps = qr. Prove that R is an equivalence relation. Also obtain the equivalence class [(3, 4)].

Question 13. Let A = {1, 2, 3, … 9} and R be the relation in A ×A defined by (a, b) R (c, d) if a + d = b + c for (a, b), (c, d) in A × A. Prove that R is an equivalence relation and also obtain the equivalent class [(2, 5)].

Question 14. Let N denote the set of all natural numbers and R be the relation on NxN defined by (a, b)R(c, d) if ad(b+c)=bd(a+c) Show that R is an equivalence relation.