Use set-builder notation to describe each set. See Example 2. (More than one description is possible.) {2, 4, 6, 8}
Table of contents
- 0. Review of College Algebra4h 45m
- 1. Measuring Angles40m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
0. Review of College Algebra
Functions
Problem 30
Textbook Question
Let A = {-6, -12⁄4, -5⁄8, -√3, 0, ¼, 1, 2π, 3, √12}. List all the elements of A that belong to each set. Whole numbers
Verified step by step guidance1
Recall the definition of whole numbers: Whole numbers are the set of numbers that include all non-negative integers starting from 0, i.e., \(\{0, 1, 2, 3, \ldots\}\).
Examine each element of the set \(A = \{-6, -\frac{12}{4}, -\frac{5}{8}, -\sqrt{3}, 0, \frac{1}{4}, 1, 2\pi, 3, \sqrt{12}\}\) to determine if it is a whole number.
Check if the element is a non-negative integer (0 or positive integer) without any fractional or irrational part.
Identify the elements that satisfy this condition: 0, 1, 3 (since \(\sqrt{12}\) is not an integer and \(2\pi\) is irrational, and the others are negative or fractions).
List these elements as the subset of \(A\) that are whole numbers: \(\{0, 1, 3\}\).
Verified video answer for a similar problem:This video solution was recommended by our tutors as helpful for the problem above
Video duration:
2mPlay a video:
0 Comments
Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Definition of Whole Numbers
Whole numbers are the set of non-negative integers starting from zero, including 0, 1, 2, 3, and so on. They do not include fractions, decimals, negative numbers, or irrational numbers. Understanding this helps identify which elements from a given set qualify as whole numbers.
Recommended video:
Multiplying Complex Numbers
Number Classification
Number classification involves categorizing numbers into sets such as integers, rational numbers, irrational numbers, and whole numbers. Recognizing the properties of each type allows for accurate sorting of elements based on their characteristics, such as sign, fractional form, or irrationality.
Recommended video:
Introduction to Complex Numbers
Simplification and Evaluation of Expressions
Simplifying expressions like fractions and radicals is essential to determine their exact value and type. For example, simplifying -12/4 to -3 or √12 to 2√3 helps decide if the number fits into the whole numbers set, which requires the number to be a non-negative integer.
Recommended video:
Evaluate Composite Functions - Special Cases
Related Videos
Related Practice
Textbook Question
21
views
