Question

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

We have, $R=\{(1,1),(1,3),(4,2),(2,4),(2,3),(3,1)\}$ is a relation on $A=\{1,2,3,4\}$, then
(a) Since, $(2,4)$ and $(2,3)\in R$, so $R$ is not a function.
(b) Since, $(4,2)\in R$ and $(2,4)\in R$ but $(4,4)\notin R$, so $R$ is not transitive.
(c) Since, $(2,3)\in R$ but $(3,2)\notin R$, so $R$ is not symmetric.
(d) Since, $(4,4),(2,2),(3,3)\notin R$, so $R$ is not reflexive.