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

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

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

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

Study Guide - Practice Questions