Reference no: EM131564035

1) Suppose C = {red, blue, white, black}. For a) and b) below, fill in two values that make the statement true (more than one solution is possible).
a) ___∈ C
b) ___∉ C

2) List the elements of the set {x | x ∈ z and x²<30}.

3) Consider U = {2, 5, blue, apple, $}, A={2, blue, $}, and B={5, $}. Complete parts a) and b) below.
a) Is A ⊆ U? Explain why or why not.
b) Is B ⊆ A? Explain why or why not.

4) Consider the following sets U, A, B, and C.

U = {mathematics, history, marketing, geography, psychology, English, finance, statistics, sociology}
A = {marketing, geography, English, statistics}
B = {mathematics, geography, psychology, English}
C = {mathematics, marketing, geography, psychology, sociology}
Compute each of the following:

a) A ∪ C =
b) C ∩ B =
    ____
c) A ∩ B =
d) A ∪ B - C =
e) A ⊕ B =

5) The records of 100 SNHU students show the following courses taken:

53 students took History
41 students took Marketing
48 students took Writing
18 students took History and Marketing
21 students took Marketing and Writing
7 students took all 3 courses
9 students took none of these courses

Answer the following questions. Show how you obtained your solution.
a) How many students took Marketing and Writing, but not History?
b) How many students took only History?

6) Consider the sequence defined by a_n = (n² - n) / 2.
a) Is this a recursive or explicit equation? Explain why.
b) Using the formula, list the first 4 terms of the sequence (starting with n=1).

This problem is similar to Examples 4-7 and to Exercises 7-14 inSection 1.3 of your textbook.

7) Consider the sequence defined by a₁ = 3 and a_n = 5 - 2a_n-1.
a) Is this a recursive or explicit equation? Explain why.
b) Using the formula, list the first 4 terms of the sequence (starting with n=1).

8) Consider the following sets.

U = {pink, purple, red, blue, gray, orange, green, yellow, indigo, violet}
A = {purple, red,orange, yellow, violet}
B = {blue, gray, orange, green}
C = {pink, red,blue, violet}

Represent each of the following sets by an array of zeros and ones. Explain your reasoning.

a) A ∪ C.
b) A ∩ B.
    ____
c) B ∪ C.

This problem is similar to Examples 12 and 13 and to Exercises 26 and 27 inSection 1.3 of your textbook.

9) Use the following matrices for the computations below.

a) Compute A + C.
b) Compute AB. If this product is undefined, explain why.
c) Compute BA. If this product is undefined, explain why.

This problem is similar to Examples 5 and 7 and to Exercise 5inSection 1.5 of your textbook.