Question

The relation $R=\left\{\right(1,1),(2,2),(3,3),(1,2),(2,3),(1,3\left)\right\}$ on set $A=\{1,2,3\}$ is

• A. reflexive but not symmetric
• B. reflexive but not transitive
• C. symmetric and transitive
• D. neither symmetric nor transitive

Answer 1

The correct option is A reflexive but not symmetric

It is reflexive because $(a,a)\in R$.

It is not symmetric.

$(a,b)\in R$

But $(b,a)\notin R$

$(1,2)\in R$ but $(2,1)\notin R$

$(1,2)\in Rand(2,3)\in R$ & $(1,3)\in R$
So, R is transitive.
So, only Option A satisfies.