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Question

Explain why every identity relation is equivalent.Give examples 


Solution

The identity relation on set E is the set {(x, x) | xϵE}
A relation R isifA relation R isifreflexivexRxirreflexivexRy implies xysymmetricxRy implies yRxantisymmetricxRy and yRx implies x=ytransitivexRy and yRz implies xRz
An equivalence relation is a relation that is reflexive, symmetric, and transitive.
Transitivity is an attribute of all equivalence relations (along with symmetric and reflexive property). Identity relation is a prime example of an equivalence relation, so it satisfies all three properties.
If a = b and b = c then obviously a = c. The formal proof of this would depend on which foundations you are building and how the identity is defined.

Mathematics

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