# Part - 4 Lecture - 2 Chapter 1 Relations and Functions

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

Booklets/Notes/Assignments are typed here on this website and their PDFs will be made available soon.

**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.