Question

Let $A=\{1,2,3,4\}$ and $R$ be a relation in $A$ is given by $R=\left\{(1,1)(2,2)(3,3)(4,4)(1,2)(2,1)(3,1)(1,3)\right\}$,Then $R$ is

• A. reflexive
• B. symmetric
• C. transitive
• D. an equivalence relation

Answer 1

Answer: (A), (B)

The correct options are
A reflexive
B symmetric

The above set contains,

$(1,2)\to (2,1)$

$(1,3)\to (3,1)$

And $(1,1)(2,2)(3,3)(4,4)$

$(2,1)$ and $(1,3)$ is present but not $(2,3)$ hence not transitive

Hence, the given relation is reflexive and symmetric.