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Question
Prove that the relation “friendship” is not an equivalence relation on the set of all people in Chennai
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Solution
(a) S = aRa
Reflexivity would require aFa for every person a ∈ P, i.e., “everyone is a friend of themselves.” In ordinary usage, a person is not considered a friend of themselves. Hence a`\cancelF`a for all a, so F is not reflexive.
(b) aRb ⇒ bRa so it is symmetric
(c) aRb, bRc does not
⇒ aRc so it is not transitive
⇒ It is not an equivalence relation
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