Question

Let $A=\{1,2,3,4\}$ and $R=\left\{\right(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(3,1),(1,3\left)\right\}$, then identify the relation $R$.

• A. reflexive
• B. symmetric
• C. transitive
• D. an equivalence relation

Answer 1

Answer: (A), (B)

The correct options are
A reflexive
B symmetric

$A=\{1,2,3,4\}$

$R=\left\{\right(1,1),(2,2),(3,3),(4,4),(1,2),(2,1),(3,1),(1,3\left)\right\}$

$R$ is reflexive since $(1,1),(2,2)$ and $(3,3$) are elements in $R$

$R$ is symmetric since $(1,2),(2,1),(3,1)$ and $(1,3)$ are elements in $R$.