Question

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

The correct option is C Not symmetric

Let $R=\left\{\right(1,3),(4,2),(2,4),(2,3),(3,1\left)\right\}$ be a relation on the set $A=\{1,2,3,4\}$, then
(a) Since $(2,4)$ $\in$ $R$ and $(2,3)$ $\in$ $R$, so $R$ is not a function.
(b) Since $(1,3)$ $\in$ $R$ and $(3,1)$ $\notin$ $R$ but $(1,1)$ $\notin$ $R$, so $R$ is not transitive:
(c) Since $(2,3)$ $\in$ $R$ but $(3,2)$ $\notin$ ${}^{\prime }R$, so $R$ is not symmetric.
(d) Since $(1,1)$ $\notin$ $R$, so $R$ is not reflexive.
Hence, option C is correct.