# 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

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

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}