Is it true that every relation which is symmetric and transitive … - Vidyadip

Question

Is it true that every relation which is symmetric and transitive is also reflexive? Give reasons.

✓

Answer

No, it is not necessary that a relation which is symmetric and transitive is reflexive as well.
For Example,
Let $A=\{a, b, c\}$ be a set and
$R_2=\{(a, a)\}$ is a relation defined on $A$.
Clearly,
$R _2$ is symmetric and transitive but not reflexive.

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