All reflexive relations are anti-symmetric

Question

Is the statement true that all reflexive relations are anti-symmetric?

Answer 1

Take base set $S=$$\left \{ 1,2,3 \right \}$

Now take  the Relation R on the Base set S ,
$R=\left \{ (1,1),(2,2),(3,3),(1,2),(2,1) \right \}$

This relation is reflexive but not anti-symmetric .

$R1=\left \{ (1,1),(2,2),(2,1) \right \}$

This relation is anti- symmetric but not reflexive .

Comments

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