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EWU Set Theory Problems

EWU Set Theory Problems


1a. Set Builder form: {x | x is a natural number and x > 4}

What is the Roster form?

1b. {14, 15, 16}

What is the set builder form?

2a. {-3, -2, -1, 0, 1, 2}

What is the set builder form?

2b. Set Builder form: {y | y is an integer and y>=-2}

What is the roster form:

3a. Let sets A and B be defined as follows.

A= {27, 26, 25, 24, –23}

B is the set of integers greater than or equal to 5 and less than or equal to 2.

Find the cardinalities of A and B.

n (A) = and n (B) =


-19 ∈ A

-2 ∈ B

-23 ∈ A

6 ∉ B

4. For each pair of sets, choose the best description.


A = {34, 35, 36}

B = {72, 73, 74}

*equivalent but not equal

*equal but not equivalent

*both equivalent and equal

*neither equivalent nor equal

4b. A is the set of even numbers greater than 9 and less than 17.

B = {10, 12, 14, 16}

*equivalent but not equal

*equal but not equivalent

*both equivalent and equal

*neither equivalent nor equal

4c. A is the set of integers greater than 2 and less than 6.

B is the set of integers greater than 2.

*equivalent but not equal

*equal but not equivalent

*both equivalent and equal

*neither equivalent nor equal

4d. A = {f, h, j, m}

B = {j, c, g}

*equivalent but not equal

*equal but not equivalent

*both equivalent and equal

*neither equivalent nor equal

Decide whether each statement is true or false.

5a. {f, h, j} ⊆ {f, h, j}

5b. {1, 4} ⊂ {1, 2, 3, 4, …}

5c. {p, q, r, s, t, u} ⊈ {p, s, u}

5d. ∅ {12, 13, 19}

6. A jazz band has three star players: Evans, Davis, and Mingus. The director can choose to have some or none, but not all, of them play in a show. In the braces below, list all the possible sets of star players that the director can have play.

Write each set in your list in roster form. If there is more than one set in your list, separate them with commas. If you need the empty set in your list, use the symbol ∅.

7. Let the set A be defined as follows.

A = {53,47,43,17,13,11,7,5}

a. Find the total number of subsets of A.

b. Find the total number of proper subsets of A.

8. For the universal set, U = {f, g, h, p, q}, complete the parts below. Write your answers in roster form or as ∅.

a. Suppose A = {f, h, p, q} . Then what is A′ ?

b. Suppose we know that B′ = {g, h}. Then what would B have to be?

9. Sets C And D are subsets of the universal set U. These sets are defined as follows.

U = { m, q, r, x, y }

C = { m, q }

D = { m, r, x}

Find the following sets. Write your answer in roster form or as ∅.

a. C∩D′ =

b. (C∪D)′ =

. =

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