Question

Let $R=\left\{\right(1,3),(4,2),(2,4\left)\right(2,3\left)\right(3,1\left)\right\}$ 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)

not symmetric

$R$ is a function as $A=\{1,2,3,4\}$ and $(2,4)\in R$ and $(2,3)\in R.$

$R$ is not reflexive $(1,1)\notin R$

$R$ is not symmetric as $(2,3)\in R.$ but $(3,2)\notin R.$

$R$ is not transitive as $(1,3)\in R$ and $(3,1)\in R$ but $(1,1)\notin R.$