Question

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

• A. a function
• B. transitive
• C. not symmetric
• D. reflexive

Answer 1

The correct option is C

not symmetric

Step 1: Explanation for the correct option.

Option C: not symmetric

A relation is symmetric if $xRy\mathrm{then}yRx$.

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

Step 2: Explanation for incorrect options.

As the set given here is $R=\left\{\left(1,3\right),\left(4,2\right),\left(2,4\right),\left(2,3\right),\left(3,1\right)\right\}$

Option A is incorrect because it is a set and not a function.

Option B: transitive

A relation is transitive if $xRy\text{and}yRz$ then $xRz$.

This relation is not transitive as $\left(1,3\right)\in R,\left(3,1\right)\in R$ but $\left(1,1\right)\notin R$.

So, option B is incorrect.

Option D: reflexive

A relation is reflexive if every element is related to itself.

This relation is not reflexive as $(1,1),(2,2),(3,3),(4,4)\notin R$.

So, option D is incorrect.

Hence, option C is correct.