Q14 – 8 points Let X = {1, 2, 3, 4, 5} and Y = {u, v, w, x, y}, and define h: X → Y as follows: h(1) = v, h(2) = x, h(3) = v, h(4) = v, h(5) = y.  (a) Draw an arrow diagram for h.  (b) Let A = {1, 4}, C = {x, y}.  Find h(A), h(X), and h−1(C).

Q1 – 9 points Let A = { h, j, k, l, m }, B = { m, n }, and C = { k, m } Is  B ⊆ A? Is  A ⊆ C? Is C a proper subset of C?

Q11- 6 points For the Venn diagram below, shade the region corresponding to the set AC ∪ C.

Q13 – 6 points Define a function F : Z × Z → Z × Z as follows: F(x, y) = (2y−1, −x) for all (x, y) in Z × Z.  Find F(0, 0) and F(2, 5).

Q11- 6 points For the Venn diagram below, shade the region corresponding to the set (A ∪ B)C.

Q1 – 9 points Let A = { j, k, l, m }, B = { m, n }, and C = { k, m } Is  B ⊆ A? Is  C ⊆ A? Is C a proper subset of C?

Q3 – 6 points Let Z be the set of all integers and let  A0 = {n ∈ Z | n = 3k, for some integer k} A1 = {n ∈ Z | n = 3k + 1, for some integer k}  and Is {A0, A1}  a partition of Z? Explain why or why not?

Q3 – 6 points Let Z be the set of all integers and let  A0 = {n ∈ Z | n = 3k, for some integer k} A1 = {n ∈ Z | n = 3k + 1, for some integer k}  and Is {A0, A1}  a partition of Z? Explain why or why not?

Q9- 6 points Use an element argument to prove the following statement: For every set A,  A ∩ ∅ = ∅.

What is the value of the maximum gains from trade? Hint: enter your answer as a number only with no $ sign Example: if the answer is $10,000, enter 10,000