Give an example of a relation which is symmetric and transitive b… - Vidyadip

Question

Give an example of a relation which is symmetric and transitive but not reflexive

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Answer

Let A = {-7, -8}
Define a relation R on A as:
R = { (-7, -7)}
Relation R is not reflexive as (a, a) $\notin$ R
Relation R is symmetric as (-7, -7) $\in$ R and (-7, -7) $\in$ R
Clearly R is transitive.
Therefore, relation R is symmetric and transitive but not reflexive.

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