Section SV.1 – Practice Problems
1. Use the roster method to list the elements of the set: The letters of the word “Mississippi”.
2. Use the roster method to list out the elements of the set “Months of the year”.
3. Write a verbal description of the set {3, 6, 9}.
4. Write a verbal description of the set {a, i, e, o, u}.
5. Write a verbal description of the set {3, 6, 9, 15, …}.
6. Which of the sets below are equal to {1, 3, 5, 7, 9}? Select all that apply. Explain your answers.
a. {1, 7, 9, 5, 3}
b. {1, 3, 5, 1, 7, 9}
c. {5, 1, 3, 1, 7, 1, 9, 1}
d. {2, 3, 7, 5, 9}
7. Which of the sets below are equal to {a, b, c, d, e}? Select all that apply. Explain your answers.
a. {d, e, b, c, a}
8. Which of the collections below are sets? (hint: Are they well defined?) Select all that apply. If the collection is not a set, explain why.
a. The collection of the funniest people in your math class.
b. The collection of everyone taller than 6 feet in your math class.
c. The college of students in your math class who completed their homework assignment.
d. The collection of students in your math class who are good drivers.
9. Which of the collections below are sets? (hint: Are they well defined?) Select all that apply. If the collection is not a set, explain why.
a. The collection of the cutest online kitten pictures.
b. The collection of college students in the United States that work at least 10 hours a week.
c. The collection of the top ten best U.S. Presidents of all time.
d. The collection of U.S. Presidents who served two terms.
10. Determine if each set below if finite or infinite.
a. The set of all stars in the Milky Way Galaxy.
b. The set of all decimal numbers between 0 and 1.
c. {1, 2, 3, …, 8, 9}
d. {5, 10, 15, 20, …}
11. Determine if each set below is finite or infinite.
a. The set of all people living in the United States.
b. The set of all fractions.
c. {1, 2, 3, …}
d. {a, b, c, …, y, z}
12. Write ⊆ or ⊈ in each blank so that the resulting statement is true.
a. {2, 4, 6} ______ {1, 2, 3, 4}
b. {2, 4, 6} ______ {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
c. {2, 4, 6} ______ {2, 4, 6, 8, 10}
d. {2, 4, 6} ______ {2, 4, 6}
e. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} ______ {2, 4, 6}
f. {2, 4, 6, 8, 10} ______ {2, 4, 6}
13. Write ⊆ or ⊂ , both, or neither in each blank so that the resulting statement is true.
a. The set of odd natural numbers greater than 7 and less than 15 ____ {9, 11, 13}
b. The set of odd natural numbers greater than 7 and less than 15 ____ {7, 9, 11,13, 15}
c. {A, B, C, D} ____ {A, B, C, D, E, F}
d. {A, B, C, D} ____ {A, B, C}
14. Is {6, 8, 10} a subset of the set of even integers?
15. Is {15, 23, 31} a subset of the set of odd integers?
16. Is the set {Earth, Moon, Mars, Saturn} a subset of the set of the planets in our solar system?
17. Is the set {A, B, C} a subset of the set of letters of the alphabet?
18. Indicate if each statement is true or false.
a. ∅ ∈ { }
b. The empty set can be written as {∅}
c. ∅ ⊆ { }
19. Consider the sets:
A = {1, 2, 3, 4, 5}
B = {1, 3, 5}
C = {4, 6}
D = {0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10}
Indicate if each statement is true or false.
a. 3 ∊ B
b. 5 ∊ C
c. B ⊂ A
d. C ⊂ A
e. C ⊂ B
f. A ⊂ D
g. A ⊂ B
20. Consider the sets:
A = {1, 3, 7}
B = {3, 5, 7, 9}
C = {1, 3, 4, 7, 8, 9}
D = {1, 3, 5, 7, 9}
Indicate if each statement is true or false.
a. 10 ∊ D
b. {7} ∊ A
c. A ⊂ C
d. A ⊂ D
e. B ⊂ C
f. B ⊂ D
g. C ⊂ D
21. For each statement, write all the symbols (⊂,⊃,⊆,⊇,∈) that, when written in the blank space, will make the statement true.
a. {Kirk} _____ {Kirk, Spock, McCoy, Uhura}
b. Kirk _____ {Kirk, Spock, McCoy, Uhura}
c. {Kirk, Spock, McCoy, Uhura} _____ {Kirk, Spock, McCoy, Uhura}
d. {Kirk, Spock, McCoy, Uhura} _____ {Spock, McCoy, Uhura}
e. { } _____ {Spock}
22. For each statement, write all the symbols (⊂,⊃,⊆,⊇,∈) that, when written in the blank space, will make the statement true.
a. { } _____ {Rocio, Lucille, Adam, Cristina}
b. {Rocio, Lucille} _____ {Adam, Cristina, Rocio, Lucille}
c. {Adam, Cristina, Rocio, Lucille} _____ {Rocio, Lucille}
d. {Rocio, Lucille, Adam, Cristina} _____ {Adam, Cristina, Rocio, Lucille}
e. Cristina _____ {Cristina}
23. Let set A represent all students currently attending college in Arizona and let set B represent all students currently attending Scottsdale Community College. Use set notation to describe the relationship between the two sets A and B.
24. Let set A represent all types of cookies, let set B represent types of cookies with chocolate chips in them, and let C represent all desserts. Indicate if each statement is true or false.
a. “sugar cookies” ∊ C
b. “sugar cookies” ∊ B
c. “chocolate cake” ∊ C
d. B ⊂ A
e. C ⊂ B
f. A ⊂ C
25. Write all the subsets of {a, b, c, d}.
26. Write all the proper subsets of {Luke, Leia, Han}.
27. Write all the proper subsets of {Stuart, Kevin, Bob}.
28. How many subsets are there of the set {Vader, Sidius, Maul, Tyranus}? How many proper subsets are there?
29. How many subsets are there of the set {Doc, Dopey, Bashful, Grumpy, Sneezy, Sleepy, Happy}? How many proper subsets are there?
30. An ice cream shop has the following set of toppings, {rainbow sprinkles, chocolate sprinkles, gummy bears, chocolate syrup, cherries, cookie crumbs}. How many different ways are there to order an ice cream sundae?
31. An Italian restaurant has the following set of toppings for their pizzas, {pepperoni, sausage, black olives, mushrooms, bell peppers, onions, anchovies}. How many different ways are there to order a pizza?
