Q2 – 9 points Let G = {1, 2, 3} and  H = {5, 6, 7} and define a relation R from G to H as follows: For every (x, y) ∈ G × H,  (x, y) ∈ R  means that  (x – y)/2  is an integer. Is 3 R 6? Is (2, 7) ∈ R? Write R  as a set of ordered pairs.  

Q3 – 6 points Let Z be the set of all integers and let  A0 = {n ∈ Z | n = 4k, for some integer k} A1 = {n ∈ Z | n = 4k + 1, for some integer k}  and A2 = {n ∈ Z | n = 4k + 2, for some integer k}. Is {A0, A1, A2}  a partition of Z? Explain why or why not?

Q5 – 6 points Let A = {p, q, r}, B = {1, 2, 4}, and C = {0, 4}. Use set-roster notation to write the following set: A × (B ∩ C)

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

Q6 – 8 points Write a proof for the following statement: For all sets A and B, if A ⊆ B, then A ⊆ A ∩ B.

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

Assume that the equilibrium price in the market for snow boots is now $500 and equilibrium quantity is now 24 snow boots.  Which of the following shifts could have resulted in this combination of equilibrium price and quantity?

Use the following information for the next 2 questions. Assume that craft beer is a normal good. Also, assume that the price of whiskey (a substitute) has increased and that the wages of craft beer employees have increased.

Assume that there are now 24 snow boots that are purchased and sold in this market (this could be the result of a government subsidy).  What is the value of wasted resources when there are 24 snow boots purchased and sold in this market? Hint: enter your answer as a number only with no $ sign Example: if the answer is $10,000, enter 10,000

In 150 to 200 words, describe the three major theoretical perspectives in Sociology. Provide an example of each.