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Question
Given an example of a relation. Which is symmetric and transitive but not reflexive.
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Solution
Let A = {–5, –6}.
Define a relation R on A as:
R = {(–5, –6), (–6, –5), (–5, –5)}
Relation R is not reflexive as (–6, –6) ∉ R.
Relation R is symmetric as (–5, –6) ∈ R and (–6, –5) ∈ R.
It is seen that (–5, –6), (–6, –5) ∈ R. Also, (–5, –5) ∈ R.
∴ The relation R is transitive.
Hence, relation R is symmetric and transitive but not reflexive.
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