Question

Let A = {1, 2, 3} and R = {(2, 2), (3, 1), (1, 3)} then the relation R on A is

• A. reflexive
• B. symmetric
• C. transitive
• D. anti-symmetric

Answer 1

Answer: (B)

symmetric

$R=\left\{\right(2,2);(3,1);(1,3\left)\right\}$

$\bullet$ not Reflective $\because (1,1)$ & $(3,3)$ absent

$\bullet$ Symm. $\because (1,3)$ & $(3,1)$ both Present

$\bullet$ not transitive $\because (3,1)\to (1,3)\Rightarrow (3,3)$

but $(3,3)$ not Present.

$\bullet$ it is symm. $\therefore$ not anti-symm.