Question
Prove that every identity relation on a set is reflexive, but the converse is not necessarily true.
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Text solutionVerified
Let
Let is an identity relation of .
Then,
So, identity relation will be reflexive.
Let be reflexive relation such that
contains and which are not elements of an identity relation.
So, it is not necessary that a reflexive relation is always an identity relation.
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Question Text | Prove that every identity relation on a set is reflexive, but the converse is not necessarily true. |
Answer Type | Text solution:1 |
Upvotes | 150 |