I attest that I am the same person as depicted in my RIT Official Photo

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?

Q9- 6 points Use an element argument to prove the following statement: For all sets A and B, if A ⊆ B, then BC ⊆ AC.

Q10- 6 points Is the following sentence a statement? Explain why or why not? If a positive integer has a negative square, then it is prime. 

I have read and understand the syllabus for this course

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, 2}, C = {x, v}.  Find h(A), h(X), and h−1(C).

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, 2}, C = {x, v}.  Find h(A), h(X), and h−1(C).

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

 Q13 – 6 points Define a function F : Z × Z → Z × Z as follows: F(x, y) = (3y−1, 1−x) for all (x, y) in Z × Z.  Find F(0, 0) and F(1, 4).

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).