**SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.**

**Describe a universal set U that includes all elements in the given sets. Answers may vary.**

1) A = {Copeland, Gershwin, Bernstein}

B = {Strauss, Mendlssohn}

2) A = {fruit juice, coffee}

B = {tea, spring water}

**MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.**

**Place the various elements in the proper regions of the Venn diagram.**

3) Let U = {8, 9, 10, 11, 12, 13, 14} and A = {8, 9, 12}. Find A’ and place the elements in the proper region.

A) A’ = {11, 12, 13, 14}

B) A’ = {8, 9, 12}

C) A’ = {8, 9, 10, 11, 12, 13, 14}

D) A’ = {10, 11, 13, 14}

4) Let U = {g, h, j, k, m, n} and A = {g, h, n}. Find A’. Then use a Venn diagram to illustrate the relationship among the sets U, A, and A’.

A) A’ = {g, h, n}

B) A’ = {g, h, m}

C) A’ = ∅

D) A’ = {j, k, m}

**Use the Venn diagram to list the elements of the set in roster form.**

5) List the elements of A.

A) {11, 13, 14, 17}

B) {13, 17}

C) {11, 12, 13}

D) {12, 15, 16}

6) List the elements of B.

A) {12, 13, 15, 16, 17}

B) {13, 17}

C) {11, 14}

D) {14, 16, 17}

7) List the elements of U.

A) {12, 15, 16}

B) {11, 14}

C) {11, 12, 13, 14, 15, 16, 17, 18, 19}

D) {13, 17}

**Use the Venn diagram to list the elements of the set in roster form.**

8) The set of students who studied Saturday

A) {Karen, Charly, Vijay}

B) {Karen, Charly, Sam, Sophia}

C) {Sam, Sophia}

D) {Karen, Charly}

9) The set of students who studied Saturday and Sunday

A) {Sam, Sophia}

B) {Karen, Charly, Kenneth, Miguel, Kavita}

C) {Sam, Sophia, Vijay}

D) {Karen, Charly, Kenneth, Miguel, Kavita, Sam, Sophia}

10) The set of students who studied Saturday and not Sunday

A) {Karen, Charly, Vijay}

B) {Sam, Sophia}

C) {Kenneth, Miguel, Kavita}

D) {Karen, Charly}

11) The set of students who studied neither Saturday nor Sunday

A) {U, Vijay}

B) {Vijay}

C) {}

D) {Vijay, Karen, Charly}

**Use the following definition to place the indicated natural number in the correct region of the Venn diagram.**

**A palindromic number is a natural number whose value does not change if its digits are reversed.**

**U = the set of natural numbers**

**A = the set of palindromic numbers**

**B = the set of odd numbers**

12) 5460

A)

B)

C)

D)

13) 1600

A)

B)

C)

D)

14) 389

A)

B)

C)

D)

15) 118

A)

B)

C)

D)

**Let U = {1, 2, 4, 5, a, b, c, d, e}. Use the roster method to write the complement of the set.**

16) Q = {2, 4, b, d}

A) {1, 3, 5, a, c, e}

B) {1, 5, a, c, e}

C) {1, 2, 4, 5, a, b, c, d, e}

D) {1, 5, a, e}

**Let U = {21, 22, 23, …, 40}, A = {21, 22, 23, 24, 25}, B = {26, 27, 28, 29}, C = {21, 23, 25, 27, …, 39}, and D = {22, 24, 26, 28, …, 40}. Use the roster method to write the following set.**

17) A’

A) A’ = {26, 27, 28, . . . , 40}

B) A’ = {27, 29, 31, . . . , 39}

C) A’ = {26, 28, 30, . . . , 40}

D) A’ = {21, 22, 23, . . . , 40}

**Let U = {21, 22, 23, 24, …}, A = {21, 22, 23, 24, …, 40}, B = {21, 22, 23, 24, …., 50} C = {22, 24, 26, 28, …,}, and D = {21, 23, 25, 27, …}. Use the roster method to write the following set.**

18) C’

A) C’ = {21, 23, 25, 27, …, 39}

B) C’ = {21, 22, 23, 24, …}

C) C’ = {21, 23, 25, 27, …}

D) C’ = {22, 24, 26, 28, …}

**Solve the problem.**

19) If the universal set is the set of the days of the week and set A is the set of days that begin with the letter T, write A’ using the roster method. Describe A’ in words.

A) A’ = {Sunday, Monday, Friday, Saturday}; A’ is the days of the week that do not begin with the letter T.

B) A’ = {Sunday, Monday, Wednesday, Friday, Saturday}; A’ is the days of the week that do not begin with the letter T.

C) A’ = {Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, Saturday}; A’ is the days of the week that do not begin with the letter T.

D) A’ = {Tuesday, Thursday}; A’ is the days of the week that begin with the letter T.

**Let U = {q, r, s, t, u, v, w, x, y, z}**

**A = {q, s, u, w, y}**

**B = {q, s, y, z}**

**C = {v, w, x, y, z}. List the elements in the set.**

20) A ∩ B’

A) {t, v, x}

B) {r, s, t, u, v, w, x, z}

C) {u, w}

D) {q, s, t, u, v, w, x, y}

21) (A ∩ B)’

A) {r, t, u, v, w, x, z}

B) {q, s, t, u, v, w, x, y}

C) {s, u, w}

D) {t, v, x}

22) C’ ∩ A’

A) {r, t}

B) {w, y}

C) {q, s, u, v, w, x, y, z}

D) {q, r, s, t, u, v, x, z}

23) A ∩ B

A) {r, t, u, v, w, x, z}

B) {q, s, y}

C) {q, s, u, w, y, z}

D) {v, w, x, y, z}

24) (A ∩ C)’

A) {w, y}

B) {q, r, s, t, u, v, w, x, y, z}

C) {q, s, y, z}

D) {q, r, s, t, u, v, x, z}

**Many children do not have access to computers at home. School has an equalizing effect. Family income is a strong factor in access. Use the information in the graph to write the set in the exercise in roster form or express the set as Ø**

25) {x | x is home access by more than 34% of the students} ∩ {x | x is school access by less than 73% of the students}

A) {$25,000 to $49,999}

B) {$75,000 or more}

C) {$50,000 to $74,999}

D) {Less than $25,000}

26) the set of home access by more than 80% of the students and school access by less than 70% of the students}

A) {$50,000 to $74,999, $75,000 or more}

B) {$50,000 to $74,999}

C) {Less than $25,000}

D) ∅

**Solve the problem.**

27) Let U = the set of the days of the week, A = {Monday, Tuesday, Wednesday, Thursday, Friday} and B = {Friday, Saturday, Sunday}. Find (A ∩ B)’.

A) {Monday, Tuesday, Wednesday, Thursday, Saturday, Sunday}

B) {Saturday, Sunday}

C) {Friday}

D) ∅

**Let U = {q, r, s, t, u, v, w, x, y, z}**

**A = {q, s, u, w, y}**

**B = {q, s, y, z}**

**C = {v, w, x, y, z}. List the elements in the set.**

28) (A ∪ B)’

A) {t, v, x}

B) {s, u, w}

C) {r, s, t, u, v, w, x, z}

D) {r, t, v, x}

29) A’ ∪ B

A) {s, u, w}

B) {q, r, s, t, v, x, y, z}

C) {q, s, t, u, v, w, x, y}

D) {r, s, t, u, v, w, x, z}

30) C’ ∪ A’

A) {s, t}

B) {w, y}

C) {q, s, u, v, w, x, y, z}

D) {q, r, s, t, u, v, x, z}

31) B ∪ C

A) {q, r, s, t, u, v, w, x, y, z}

B) {v, w, x, y, z}

C) {q, s, u, w, y}

D) {q, s, v, w, x, y, z}

32) C ∪ ∅

A) {q, s, y, z}

B) {}

C) {q, s, u, w, y}

D) {v, w, x, y, z}

33) B ∪ U

A) {q, s, u, w, y}

B) {v, w, x, y, z}

C) {q, r, s, t, u, v, w, x, y, z}

D) {q, s, y, z}

**Many children do not have access to computers at home. School has an equalizing effect. Family income is a strong factor in access. Use the information in the graph to write the set in the exercise in roster form or express the set as Ø**

34) {x | x is home access by more than 34% of the students} ∪ {x | x is school access by less than 81% of the students}

A) {Less than $25,000, $75,000 or more}

B) {$25,000 to $49,999, $50,000 to $74,999}

C) {$50,000 to $74,999, $75,000 or more}

D) {Less than $25,000, $25,000 to $49,999}

35) the set of home access by more than 80% of the students or school access by less than 87% of the students}

A) {$25,000 to $49,999, $50,000 to $74,999, $75,000 or more}

B) {Less than $25,000, $25,000 to $49,999, $50,000 to $74,999}

C) {Less than $25,000, $25,000 to $49,999}

D) {$50,000 to $74,999, $75,000 or more}

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