3. Consider the poset (Z,I) a) Draw the Hasse Diagram for (S, ), where s (2, 3, 4, 5, 6, 9, 12, 15. b) Find the minimal, maximal, least, and greatest elements of ( S) ) c) Find the lower bounds, greatest lower bound, upper bounds, and least upper bound of ( S, I) with respect to (T,1)where T (1,2,3,...500 d) is (S, 1) a total order ? Is (S, I)a lattice? Justify your answers