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 or transitive

Answer 1

The correct option is A Reflexive but not symmetric

GIven $A=\{1,2,3\}$ and $R=\left\{\right(1,1),(2,2),(3,3),(1,2),(2,3),(1,3\left)\right\}$

A relation $R$ in $A$ is said to be reflexive, if $(a,a)\in R$ for every $a\in A$.

Since $(1,1),(2,2),(3,3)\in R$ , $R$ is reflexive.

A relation $R$ in $A$ is said to be symmetric, if $(a_1,a_2)\in R⟹(a_2,a_1)\in R$ for $a_1,a_2\in A$.

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

$(2,3)\in R$ But $(3,2)\notin R$

$(1,3)\in R$ But $(3,1)\notin R$

Hence $R$ is not symmetric.