Q9-5 points Use the roster method to describe the set  { 4n + 1 | n ∈ ℤ }.

Q10-5 points Michael has five different sport coats hanging on a closet rod. In how many ways can they be arranged? 

Q15-5 points Make a Venn Diagram that illustrates the set (​A​ ​∪​ B​) ∩ C.

Q6-12 points Define functions  ​f​ , ​g​ , ​h​  from {1, 2, 3, 4} to {​a​, ​b​, ​c​, ​d​} as follows: f (1) = a,  f (2) = d, f (3) = c g(1) = a,  g(2) = a, g(3) = b,  g(4) = b h(1) = d,  h(2) = a, h(3) = c, h(4) = b                                                                                             Which of these functions are well-defined? ​                                                                                                                                              Which of these functions are onto?                      Which of these functions are one-to-one?         

Q1-5 points Given the following sets: U = ​{1, 2, 3, 4, 5, 6, 7, 8} A = ​{4, 6, 7} B = ​{1, 2, 4, 7} C = ​{1, 3, 5, 6, 8} Find C U B.

Q11-5 points How many (5 digit) U.S. zip codes are possible, assuming that every possible 5-digit sequence can be used as a valid zip code?

Q17-5 points Solve by backtracking for an explicit formula for the recursive sequence: a1​ = 4 an​ = -3a​n-1

Q16-5 points Use the Binomial Theorem to write out the expansion of (a + b)4 .

Q13-5 points Jim has a drawer with 6 red socks, 6 blue socks, and 10 black socks. If he picks them out without looking, how many socks must Jim pull out of the drawer to guarantee that he has a matching color pair?

Q19-5 points Consider the sequence: 1, 7, 13, 19, 25, … Find both the 50th term of the sequence and the sum of the first 50 terms.