Question

Show that the relation R in the set A of all books in a library of a college, given by R = {(x, y): x and y have the same number of pages} is an equivalence relation.

Answer 1

(i) The number of pages in a book remain the same.

⇒ Relation R is reflexive.

(ii) The book x has the same number of pages as the book y.

⇒ Book y has the same number of pages as the book x.

⇒ The relation R is symmetric.

(iii) Books x and y have the same number of pages.

⇒ Also books y and z have the same number of pages.

⇒ Books x and z also have the same number of pages.

⇒ R is transitive also.

Thus, R is an equivalence relation.