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 on a set is said to be an equivalence relation if it is reflexive, symmetric and transitive relation.
The given relation is defined by
{ a is cousin of b}
But here the relation is not reflexive
as .
Because if , then is cousin of which is not true.
As the relation is not reflexive , therefore the given relation is not an equivalence relation on the set of all human being.