Question

Let $A=\{1,2,3\}$ and let $R=A\times A$ then what is the relation $R$ on $A$.

• A. reflexive
• B. symmetric
• C. transitive
• D. not reflexive

Answer 1

Answer: (A), (B), (C)

reflexive
transitive
symmetric

$A=\{1,2,3\}$

$A$ $\times$ $A$ $=\left\{\right(1,1),(1,2),(1,3),(2,1),(2,2),(2,3),(3,1),(3,2),(3,3\left)\right\}$.

$R$ is reflexive since $(a,a)$ $\in$ $R$ $\forall a\in A$.

$R$ is symmetric since $(a,b)$ $\in$ $R$ and $(b,a)$ $\in$ $R$, $\forall a,b\in A$.

$R$ is transitive since$(a,b)$, $\in$ $R,(b,c)$ $\in$ $R,(a,c)$ $\in$ $R$, $\forall a,b,c\in A$.