giva an example of a relation which is symmetric but neither reflexive nor transitive
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∴ R is not reflexive. ... Relation R is symmetric since (a, b) ∈ R ⇒ (b, a) ∈ R for all a, b ∈ R. Relation R is not transitive since (4, 6), (6, 8) ∈ R, but (4, 8) ∉ R. Hence, relation R is reflexive and symmetric but not transitive.
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Let A={5,6,7}
Define a relation R on A as R={(5,6),(6,5)}
Relation R is not reflexive as (5,5),(6,6),(7,7)∈
/
R.
Now, as (5,6)∈R and also (6,5)∈R, R is symmetric.
⇒(5,6),(6,5)∈R, but (5,5)∈
/
R
∴R is not transitive.
Hence, relation R is symmetric but not reflexive or transitive.
Step-by-step explanation:
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