Question 1

Which of the following best describes the empty set ($$\emptyset$$)?

Accepted Answer

A set containing no elements at all.

Question 2

Given $$U = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$$, $$A = \{1, 2, 3, 4, 5\}$$, and $$B = \{2, 4, 6, 8\}$$, what is $$A \cap B$$?

Accepted Answer

$$\{2, 4\}$$

Question 3

Which of the following sets is NOT well defined?

Accepted Answer

The set of all large cities in the world.

Question 4

If $$A = \{red, blue\}$$, which of the following is a proper subset of $$A$$?

Accepted Answer

$$\{red\}$$

Question 5

Given $$U = \{a, b, c, d, e, f, g\}$$, $$M = \{a, b, d\}$$, and $$N = \{b, d, f\}$$, what is $$M \cup N$$?

Accepted Answer

$$\{a, b, d, f\}$$

Question 6

Which of the following statements is TRUE about subsets?

Accepted Answer

The empty set is a subset of every set.

Question 7

Given $$U = \{11, 12, 13, 14, 15, 16\}$$ and $$A = \{12, 15, 16\}$$, what is $$A' ($$the complement of $$A$$)?

Accepted Answer

$$\{11, 13, 14\}$$

Question 8

If $$A = \{1, 3, 5, 7, 9\}$$ and $$B = \{7, 9, 11, 13\}$$, what is $$A \cup B$$?

Accepted Answer

$$\{1, 3, 5, 7, 9, 11, 13\}$$

Question 9

Which of the following is the correct roster method for the set of prime numbers less than 15?

Accepted Answer

$$\{2, 3, 5, 7, 11, 13\}$$

Question 10

A survey of 150 students found that 95 read fiction, 70 read non-fiction, and 32 read both. How many students read only fiction?

Accepted Answer

$$63$$

Question 11

Given $$U = \{1, 2, 3, \ldots, 20\}$$, $$E = \{2, 4, 6, \ldots, 20\}$$, and $$F = \{5, 10, 15, 20\}$$, what is $$E \cap F$$?

Accepted Answer

$$\{10, 20\}$$

Question 12

Which of the following is a true statement about the relationship between a set and its complement?

Accepted Answer

The union of a set and its complement is the universal set.

Question 13

If $$A = \{1, 2, 3, 4, 5\}$$, $$B = \{0, 2, 4, 6, 8\}$$, and $$C = \{2, 3, 5, 7, 8\}$$, what is $$A \cap B \cap C$$?

Accepted Answer

$$\{2\}$$

Question 14

Which of the following is an example of a set that is NOT a proper subset of $$\{a, b, c\}$$?

Accepted Answer

$$\{a, b, c\}$$

Question 15

A small shop recorded that 28 customers bought T-shirts, 20 bought caps, 9 bought both, and 23 bought neither. How many customers bought only a T-shirt?

Accepted Answer

$$19$$

Question 16

Given $$U = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$$, $$A = \{1, 2, 3, 4, 5\}$$, what is $$A'$$?

Accepted Answer

$$\{0, 6, 7, 8, 9\}$$

Question 17

Which of the following statements about Venn diagrams is correct?

Accepted Answer

The intersection of two sets $$A$$ and $$B is $$represented by the overlapping region of their circles.

Question 18

If $$A = \{1, 2, 3\}$$ and $$B = \{3, 4, 5\}$$, what is $$A \cup B$$?

Accepted Answer

$$\{1, 2, 3, 4, 5\}$$

Study Guide: Sets and Set Operations in Liberal Arts Mathematics

Study Guide - Practice Questions

Study Guide - Flashcards