Mathematics - Sets and Relations Question with Solution | TestHub

Let $\mathrm{R}=\{(3,3),(5,5),(9,9),(12,12),(5,12)$, $(3,9),(3,12),(3,5)\}$ be a relation on set $\mathrm{A}=\{3,5,9,12\}$ Clearly, every element of $A$ is related to itself. Therefore, it is a reflexive. Now, $\mathrm{R}$ is not symmetry because 3 is related to 5 but 5 is not related to 3 . Also $\mathrm{R}$ is transitive relation because it satisfies the property that if $a\mathrm{R}b$ and $b\mathrm{R}c$ then $a\mathrm{R}c$.