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