Question

Let $A=\{a,b,c\}$ and $\left\{\right(a,a),(b,b),(c,c),(b,c),(a,b\left)\right\}$ be a relation on A, then R is:

• A. symmetric
• B. transitive
• C. reflexive
• D. anti-symmetric

Answer 1

Answer: (C)

reflexive

Here, $R$ is reflexive as $xRx$ for all $x$ in$A$.

since, $(a,b)\in R$ but $(b,a)\notin R$, therefore, $R$is not symmetric.

Again $(a,b),(b,c)\in R$ but $(a,c)\notin R$, therefore, $R$ is not transitive.