Question

Let R = {(1, 3), (4, 2), (2, 4), (2, 3), (3, 1)} be a relation on the set $ A=\{1,2,3,4\} $ . The relation R is

• A. a function
• B. transitive
• C. not symmetric
• D. reflexive

Answer 1

Answer: (C)

Let R = {(1, 3), (4, 2), (2, 4), (2,3), (3,1)} is a relation on the set $ A=\{1,\text{ }2,\text{ }3,\text{ }4\}, $ then (a) Since $ (2,4)\in R $ and $ (2,3)\in R, $ so R is not a function. (b) Since $ (1,3)\in R $ and $ (3,1)\in R $ but $ (1,1)\cancel{\in }R $ . So R is not transitive. (c) Since $ (2,3)\in R $ but $ (3,2)\cancel{\in }R, $ so R is not symmetric. (d) Since $ (4,4)\cancel{\in }R, $ so R is not reflexive, Hence the option is correct.