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Archangel Macsika

Check whether the relation defined by{(a,b)}| a is cousin of b}defined on the sets of all human being is an equivalence or not?

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A relation R on a set is said to be an equivalence relation if it is reflexive, symmetric and transitive relation.

The given relation is defined by

R= {(a,b): a is cousin of b}

But here the relation R is not reflexive

as (a,a)\notin R .

Because if (a,a)\in R , then a is cousin of a. which is not true.

As the relation R is not reflexive , therefore the given relation R is not an equivalence relation on the set of all human being.


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