Question

Let $R=\left\{(1,3),(4,2),(2,4),(2,3),(3,1)\right\}$ be relation on the set $A=\{1,2,3,4\}$. The relation $R$ is

• A. Reflexive
• B. Transitive
• C. Not symmetric
• D. A function

Answer 1

The correct option is C

Not symmetric

Explanation for the correct option:

Finding the relation of $R$

Given $R=\left\{(1,3),(4,2),(2,4),(2,3),(3,1)\right\}$ is a relation on set $A=\{1,2,3,4\}$

(a)Since $(2,4)\in R$ and $(2,3)\in R$, so $R$ is not a function.

If $(a,b)\in R\text{and}(b,c)\in R\text{then}(a,c)\in R$ then $R$ is transitive
(b) Since$(1,3)\in R\text{and}(3,1)\in R\mathrm{but}(3,3)\notin R,$ so $R$ is not transitive:

If $(a,b)\in R\text{then}(b,a)\in R$ then $R$ is symmetric
(c) Since $(2,3)\in R$ but $(3,2)\notin R$, so $R$ is not symmetric.
If $(a,a)\in R$ Then $R$ is reflexive

(d)Since $(1,1)\notin R,$ so $R$ is not reflexive.

Hence, the correct option is (C)