 Hello and welcome to the session. Let us discuss the following problem today. Show that the relation r and r defined as r is equal to a, b such that a is less than equal to b is reflexive and transitive but not symmetric. Now let us write the solution we have. r is equal to a, b such that a is less than equal to b where a, b belongs to r. Now let us check for reflexivity. For any element a belongs to r we have a less than equal to a therefore a, a belongs to r for all a belongs to r therefore r is reflexive. Now let us check for symmetry. For elements 2 and 3 belong to r we have 2 less than equal to 3 but 3 is not less than equal to 2 therefore 2, 3 belongs to r but 3, 2 does not belong to r therefore r is not symmetric. Now let us check for transitivity. Let a b belongs to r, b c belongs to r that is a is less than equal to b and b is less than equal to c which implies a is less than equal to c which implies a, c belongs to r therefore r is transitive. Hence we have proved r is reflexive, r is not symmetric and r is transitive. I hope you understood this problem. Bye and have a nice day.