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

“Many of life’s failures are people who did not realize how close they were to success when they gave up.” —*Thomas A. Edison*

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**Question 6.** Let A = {0, 1, 2, 3} and define a relation R on A as follows: R = {(0, 0), (0, 1), (0, 3), (1, 0), (1, 1), (2, 2), (3, 0), (3, 3)}. Is R reflexive? symmetric? transitive? **(E)**

**Question 7.** Let R be the relation in the set {1, 2, 3, 4} given by R = {(1, 2), (2, 2), (1, 1), (4,4), (1, 3), (3, 3), (3, 2)}. Choose the correct answer. **(N)** **A.** R is reflexive and symmetric but not transitive. **B.** R is reflexive and transitive but not symmetric. **C.** R is symmetric and transitive but not reflexive. **D.** R is an equivalence relation.

**Question 8.** Check whether the relation R defined in the set {1, 2, 3, 4, 5, 6} as R = {(a, b) : b = a + 1} is reflexive, symmetric or transitive. **(N)**

**Question 9.** Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive. **(N)**