Question: 11. (a) Given the set A = {1, 2, 3} and the set S = {(x, y) | x and y in A}. Consider the

11.

(a) Given the set A = {1, 2, 3} and the set S = {(x, y) | x and y in A}. Consider the relation defined on S as follows: ((x1, y1) (x2, y2) if x1 x2 and y1 y2. Draw the directed graph of this relation. Show that it is a partial order. Explain why it is not a total order.

(b). Consider the set S defined in problem 4 and the following relation = defined on S as follows: (x1, y1) = (x2, y2) if x1 + y1 = x2 + y2. Draw the directed graph of this relation. Show that it is an equivalence relation. List its equivalence classes.

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