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 $A=\{1,2,3,4\},$ 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.