# Q.7 Show that the relation R in the set A of all the books in a library of a college, given by is an equivalence relation.￼

A = all the books in a library of a college

because  x and x have same number of pages so it is reflexive.

Let    means x and y have same number of pages.

Since,y and x have same number of pages so    .

Hence, it is symmetric.

Let    means x and y have same number of pages.

and    means y and z have same number of pages.

This states,x and z also have same number of pages i.e.

Hence, it is transitive.

Thus, it is reflexive, symmetric and transitive i.e. it is an equivalence
relation.?

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