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

“I alone cannot change the world, but I can cast a stone across the water to create many ripples.” —*Mother Teresa*

**Question 1.** Determine whether each of the following relations are reflexive, symmetric and transitive:**(N)****A.** Relation R in the set

A = {1, 2, 3, …, 13, 14} defined as R = {(x, y) : 3x – y = 0}**B.** Relation R in the set N of natural numbers defined as R = {(x, y): y = x + 5 and x < 4}**C.** Relation R in the set A = {1, 2, 3, 4, 5, 6} as R = {(x, y) : y is divisible by x}**D.** Relation R in the set Z of all integers defined as R = {(x, y) : x – y is an integer}**E.** Relation R in the set A of human beings in a town at a particular time given by **a.** R = {(x, y) : x and y work at the same place} **b.** R = {(x, y) : x and y live in the same locality} **c.** R = {(x, y) : x is exactly 7 cm taller than y}**d.** R = {(x, y) : x is wife of y} **e.** R = {(x, y) : x is father of y}