Hello, I have discrete math questions.

I need your help.

Thank you so much.

Please, draw it by handwriting when you are asked for drawing.

Please, draw it by handwriting when you are asked for drawing.

8. Let A = Z X Z and consider the relation R on A dened by (a, b)R(c, d) if and only if a S c and b 2 d. (a) [3 marks] Show that (A72) is a poset. (b) [2 marks] Now consider B = {1,2, 3} x {4, 5}. Using the same relation R as in the setup above, it is true that R is a partial order on B (you do not need to prove this). Draw the Hasse diagram for the poset (3,72). (0) [1 mark] Using your Hasse diagram in part (b), is the relation R a total order on B? Explain. 9. [2 marks each] (a) Draw the Hasse diagram for the partial order where R is the relation \"divides\" on the set A = {2,3,5, 10,12,45,60,90, 180}. (i.e. mRy if and only if 33kg) (b) Draw the Hasse diagram for the partial order where R is the \"subset\" relation on the set A = {{1},{2}, {1,3}, {2,4}, {1,2,3}, {1,2,3,4}}. (i.e. XRY if and only if X Q Y.) (C) Draw the Hasse diagram for the partial order where R is the relation on the set A = {1, 2, 3, 4, 5} with R = {(1,1)(2,2),(333),(4,4),(5,5),(1,3),(2,1),(2,3),(2,5),(4,1),(42),(4,3),(4,5),(5,3)}- (d) Give a total order on A = {1, 2, 3, 4, 5} that contains the relation R from part (c)