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

**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. R_{1} = {(a, b) : a, b are ages of students and |a – b| 0} R_{2} = {(a, b) : a, b are weights of students, and |a – b| 0} R_{3} = {(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)**