 Hello and welcome to the session. Let us discuss the following problem today. Show that the relation r in the set A of all books in a library of a college given by r is equal to x, y, z that x and y have same number of pages is an equivalence relation. Now let us write the solution. Given to us is A is equal to all books in a library. Now relation r is equal to x, y, z that x and y have same number of pages. Now let us check for reflexivity. Clearly, x, x belongs to r. Therefore, r is reflexive. Now let us check for symmetry. We have x, y belongs to r and y, x belongs to r. Since number of pages in x is equal to number of pages in y. Therefore, r is symmetric. Now let us check for transitivity. Let x, y belongs to r and y, z belongs to r. That is, number of pages in x is equal to number of pages in book y and number of pages in book y is equal to number of pages in book z which implies number of pages in book x is equal to number of pages in book z which implies x, z belongs to r. Therefore, r is transitive. Now since r is symmetric, reflexive and transitive. Therefore, r is an equivalence relation. I hope you understood this problem. Bye and have a nice day.