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Question
Give an example of a relation which is symmetric but neither reflexive nor transitive?
Solution
Let A = {5, 6, 7}.
⇒ And the relation R = {(5, 6), (6, 5)}.
The relation R is not reflexive because (5, 5), (6, 6), and (7, 7) ∉ R.
∴ R is not reflexive
⇒ Now, since (5, 6) ∈ R and (6, 5) ∈ R,
∴ R is symmetric.
⇒ (5, 6), (6, 5) ∈ R, but (5, 5) ∉ R
∴ R is not transitive.
Hence, the relation R is symmetric but neither reflexive nor transitive.
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