Question

Let $A=\{1,2,3\}$ and $R,S$ be two relations on $A$ given by $R=\left\{\right(1,1),(2,2),(3,3),(1,2),(2,1\left)\right\},S=\left\{\right(1,1),(2,2),(3,3),(2,3),(3,2\left)\right\}$ then $R\cup S$ is

• A. Reflexive, symmetric and transitive relation
• B. reflexive and transitive relation only
• C. not a transitive relation
• D. Reflexive relation but not Symmetric relation

Answer 1

The correct option is C not a transitive relation

$R\cup S=\left\{\right(1,1),(2,2),(3,3),(1,2),(2,1),(2,3),(3,2\left)\right\}$

$\therefore$ It is reflexive, symmetric but not transitive because $(1,2),(2,3)\in R\cup S$ but $(1,3)\notin R\cup S$.