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Question
Given an example of a relation. Which is
(v) Symmetric and transitive but not reflexive.
Given an example of a relation. Which is
(v) Symmetric and transitive but not reflexive.
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Solution
Let A ={-5,-6}
Define a relation R on A as: R ={(-5,-6),(-6,-5),(-5,-5)}
Relation R is not reflexive as (−6,−6)/∈R
Relation R is symmetric as (−5,−6)∈R and (−6,−5)∈R.
And (−5,−6),(−6,−5)∈R⇒(−5,−5)∈R.
Therefore, the relation R is transitive.
Hence, relation R is symmetric and transitive but not reflexive.
Let A ={-5,-6}
Define a relation R on A as: R ={(-5,-6),(-6,-5),(-5,-5)}
Relation R is not reflexive as (−6,−6)/∈R
Relation R is symmetric as (−5,−6)∈R and (−6,−5)∈R.
And (−5,−6),(−6,−5)∈R⇒(−5,−5)∈R.
Therefore, the relation R is transitive.
Hence, relation R is symmetric and transitive but not reflexive.
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