Question

Let $R=\left\{\right(3,3),(6,6),(9,9),(6,12),(3,9),(3,12),(3,6\left)\right\}$ be a relation on the set $A=\{3,6,9,12\}.$ Then the relation $R^{-1}$ is

• A. reflexive and transitive.
• B. not symmetric
• C. transitive
• D. all the above

Answer 1

Answer: (A)

reflexive and transitive.

$\begin{array}{c}Wehave\\ R=\left\{\left(3,3\right),\left(6,6\right)\left(9,9\right)\left(12,12\right),\left(6,12\right),\left(3,12\right),\left(3,6\right)\right\}\\ and,\\ A=\left\{3,6,9,12\right\}\\ Then\\ Therelationisreflexiveandtransitiveonly.because\\ \left\{\left(3,3\right),\left(6,6\right)\left(9,9\right)\left(12,12\right)\right\}itisReflexive\\ and,\left(6,12\right),\left(3,12\right),\left(3,6\right)\left[itistransitive.\right]\end{array}$

Hence, option $A$ is the correct answer.