Question

The relation $R=\left\{\right(1,1),(2,2),(3,3\left)\right\}$ on the set $\{1,2,3\}$ is

• A. Symmetric only
• B. Reflexive only
• C. An equivalence relation
• D. transitive only

Answer 1

The correct option is C An equivalence relation

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

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

AS $aRa\forall a\in A$ R is reflexive.

R is symmetric if $aRb\Rightarrow bRa$

here no such element so we take R as symmetric (There is no element like (1,2) in R)

R is transitive if $aRbandbRc\Rightarrow aRc$

Again there no element (1,2) and (2,3) in R so no such casesto check so we can say R is Transitive.