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

“We know what we are, but know not what we may be.” —William Shakespeare

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

Question 1. Let R be the relation in the set N given by R = {(a, b) : a = b – 2, b 6}. Choose the correct answer. A. (2, 4) ∈ R B. (3, 8) ∈ R C. (6, 8) ∈ R D. (8, 7) ∈ R (N)

Question 2. Let A= {1, 2, 3,} and define R = {(a, b): a – b = 12}. Show that R is empty relation on Set A. (B)

Question 3. Let A be the set of all students of a boy’s school. Show that the relation R in A given by R = {(a, b) : a is sister of b} is the empty relation and R′ = {(a, b) : the difference between heights of a and b is less than 3 meters} is the universal relation. (N)

Question 4. If A is the set of students of a school then write, which of following relations are Universal, Empty or neither of the two. R1 = {(a, b) : a, b are ages of students and |a – b| 0} R2 = {(a, b) : a, b are weights of students, and |a – b| 0} R3 = {(a, b) : a, b are students studying in same class} (B)

Question 5. Let A = {1, 2, 3,} and define R = {(a, b): a + b 0}. Show that R is a universal relation on set A. (B)