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Question
Given an example of a relation. Which is
(iii) Reflexive and symmetric but not transitive.
Given an example of a relation. Which is
(iii) Reflexive and symmetric but not transitive.
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Solution
Let A ={4,6,8}
Define a relation R on A as A
={(4,4),(6,6),(8,8),(4,6),(6,4),(6,8),(8,6)}
Relation R is reflexive, because (4,4),(6,6), (8,8)∈R.
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
Let A ={4,6,8}
Define a relation R on A as A
={(4,4),(6,6),(8,8),(4,6),(6,4),(6,8),(8,6)}
Relation R is reflexive, because (4,4),(6,6), (8,8)∈R.
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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