 Hello and welcome to the session and I will discuss the following problem today. Check whether the relation r defined in the set 1, 2, 3, 4, 5, 6 as r is equal to a, b such that b is equal to a plus 1 is reflexive, symmetric or transitive. Now let us write the solution. Given to us is relation r is equal to a, b such that b is equal to a plus 1. Define in the set a is equal to 1, 2, 3, 4, 5, 6. Now let us check for reflexivity. We have the relation r is equal to 1, 2, 2, 3, 3, 4, 4, 5 and 5, 6. So for reflexivity we have for 1 belongs to a, 1, 1 does not belongs to r. Therefore, r is not reflexive. Now checking for symmetry. We have 1, 2 belongs to r but 2, 1 does not belongs to r. Therefore, r is not symmetric. Now let us check for transitivity. We have 1, 2 belongs to r and 2, 3 belongs to r but 1, 3 does not belongs to r. Therefore, r is not transitive. Hence r is not reflexive, r is not symmetric and r is not transitive. I hope you understood this problem. Bye and have a nice day.