Q1-8 points Let ​A​ = {1, 2, 3, 4} and let ​R​ be the following relation from ​A ​to​ A​: R​ = {(1, 1), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 4), (4, 3)} ​                                                                                                                        Create the digraph for this relation. Create the matrix ​MR​ ​for this relation. ​

Q16-5 points Use the Binomial Theorem to write out the expansion of (2a + b)3 .

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

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.

 Q13-5 points Jim has a drawer with 6 red socks, 6 blue socks, and 8 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?

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?

Q18-5 points Solve the recurrence relation: b1​ = 3 b2​ = 5 bn​ = 2​bn-1​ −​ b​n-2

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?

Q12-5 points Jamar’s Donut Shop sells 6 flavors of doughnuts each day. If repeat flavors are allowed, how many different ways can a three-doughnut box be filled?

Q14-5 points 19,596 people attended the second game of the 2017 NBA Finals between the Golden State Warriors and the Cleveland Cavaliers. Is it a certainty that at least two of those people shared the same three-letter set of initials (such as JFK or LBJ)? Justify your reasoning.