Let $R=\{(3,3)(5,5),(9,9),(12,12),(5,12),(3,9)$, $(3,12),(3,5)\}$ be a relation on the $\operatorname{set}…
Let $R=\{(3,3)(5,5),(9,9),(12,12),(5,12),(3,9)$, $(3,12),(3,5)\}$ be a relation on the $\operatorname{set} A=\{3,5,9,12\}$. Then, $R$ is :
reflexive, symmetric but not transitive.
symmetric, transitive but not reflexive.
an equivalence relation.
reflexive, transitive but not symmetric.
Solution
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 $a \mathrm{R} c$.