$$E = \{x \mid x \text{ is an even integer}\}$$

$$H = \{x \mid x \text{ is a small apple}\}$$

$$N = \{x \mid x \text{ is a negative integer}\}$$

Question 1

Which of the following best describes a 'well-defined' set?

Accepted Answer

A set where there is no ambiguity about which elements belong.

Question 2

Given the set $$S = \{0, 1, 2, 3, 4, 5, 6, 7, 8, 9\}$$, which statement is true?

Accepted Answer

S is a finite set.

Question 3

Which of the following is the correct notation for the empty set?

Accepted Answer

$$\emptyset$$

Question 4

Suppose $$A = \{x \mid x 	ext{ is a positive integer}\}. $$What type of set is $$A$$?

Accepted Answer

Infinite set

Question 5

Which of the following sets is NOT well-defined?

Accepted Answer

The set of all small apples in a barrel.

Question 6

If $$E is $$the empty set, which of the following is true?

Accepted Answer

$$E$$ contains no elements.

Question 7

Which of the following is a correct way to write the set of all positive integers?

Accepted Answer

$$P = \{1, 2, 3, 4, 5, \ldots\}$$

Question 8

Which of the following is an example of a finite set?

Accepted Answer

The set of all students in a classroom.

Question 9

A set $$B is $$defined as $$B = \{x \mid x 	ext{ is a digit from 0 to 9}\}. $$How many elements does $$B$$ have?

Accepted Answer

10

Question 10

Which of the following best describes the set $$C = \{x \mid x 	ext{ is a solution to } x^2$ = -1\}$$?

Accepted Answer

C is the empty set if considering only real numbers.

Question 11

Which notation correctly represents a set containing no elements?

Accepted Answer

$$\emptyset$$

Question 12

If $$D = \{x \mid x 	ext{ is a prime number less than 10}\}$$, which of the following is $$D$$?

Accepted Answer

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

Question 13

Which of the following sets is infinite?

Accepted Answer

The set of all positive integers.

Question 14

Suppose $$F = \{x \mid x 	ext{ is a solution to } x^2$ = 4\}. $$What is $$F$$?

Accepted Answer

$$\{2, -2\}$$

Question 15

Which of the following is a valid set notation for the set of all even numbers?

Accepted Answer

$$E = \{x \mid x 	ext{ is an even integer}\}$$

Question 16

A set $$G is $$defined as $$G = \{x \mid x 	ext{ is a solution to } x^2$ = 0\}. $$What is $$G$$?

Accepted Answer

$$\{0\}$$

Question 17

Which of the following is NOT a valid set notation?

Accepted Answer

$$H = \{x \mid x 	ext{ is a small apple}\}$$

Question 18

If $$J = \{x \mid x 	ext{ is a solution to } x^2$ = 9\}$$, what is $$J$$?

Accepted Answer

$$\{3, -3\}$$

Question 19

Which of the following sets is a singleton set?

Accepted Answer

The set $$K = \{0\}.$$

Question 20

Which of the following is the correct way to write the set of all negative integers?

Accepted Answer

$$N = \{x \mid x 	ext{ is a negative integer}\}$$

Essential Prerequisites: Sets and Set Notation in College Algebra

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