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Question
Give an example of a relation which is symmetric and transitive but not reflexive?
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Solution
Let A = {−5, −6}
The relation R on a set A is defined as follows:
R = {−5, −6), (−6, −5), (−5, −5)}
The relation R is not reflexive because (−6, −6) ∉ R.
∴ R is not reflexive.
⇒ The relation R is symmetric because (−5, −6) ∈ R and (−6, −5) ∈ R.
∴ R is symmetric.
⇒ And, if (−5, −6) and (−6, −5) ∈ R, then (−5, −5) ∈ R
∴ R is transitive.
Hence, the relation R is symmetric and transitive but not reflexive.
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