Table of contents

0. Review of Algebra4h 18m
1. Equations & Inequalities3h 18m
2. Graphs of Equations43m
3. Functions2h 17m
4. Polynomial Functions1h 44m
5. Rational Functions1h 23m
6. Exponential & Logarithmic Functions2h 28m
7. Systems of Equations & Matrices4h 6m
8. Conic Sections2h 23m
9. Sequences, Series, & Induction1h 22m
10. Combinatorics & Probability1h 45m

0. Review of Algebra

Exponents

College Algebra

0. Review of Algebra

Exponents

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2:09 minutes

Problem 19

Textbook Question

Use set notation, and list all the elements of each set. {12, 13, 14,..., 20}

Verified step by step guidance

Identify the pattern in the given set: {12, 13, 14, ..., 20}.

Recognize that the set is a sequence of consecutive integers starting from 12 and ending at 20.

List all the elements of the set by continuing the sequence: 12, 13, 14, 15, 16, 17, 18, 19, 20.

Use set notation to express the complete set: {12, 13, 14, 15, 16, 17, 18, 19, 20}.

Verify that all elements from the starting number (12) to the ending number (20) are included in the set.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Set Notation

Set notation is a mathematical way to describe a collection of distinct objects, known as elements. It typically uses curly braces to enclose the elements, such as {a, b, c}. Understanding set notation is essential for identifying and listing elements within a set, as well as for performing operations like unions and intersections.

Element Listing

Element listing involves explicitly writing out all the members of a set. For example, the set {12, 13, 14, ..., 20} indicates a sequence of integers from 12 to 20. This concept is crucial for accurately representing the contents of a set and ensuring clarity in mathematical communication.

Set Representation

Set representation can be done in various forms, including roster form and set-builder notation. Roster form lists all elements explicitly, while set-builder notation describes the properties that define the elements of the set. Understanding these representations helps in interpreting and manipulating sets effectively in algebra.