Question

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?

Answer 1

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.