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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0:47 minutes

Problem 43

Textbook Question

Determine whether each statement is true or false. 9 ∉ {8, 5, 2, 1}

Verified step by step guidance

Identify the elements in the set \( \{8, 5, 2, 1\} \).

Check if the number 9 is present in the set.

Since 9 is not listed among the elements of the set, determine the relationship between 9 and the set.

Understand that the symbol \( \notin \) means 'is not an element of'.

Conclude that the statement '9 \( \notin \) \{8, 5, 2, 1\}' is true.

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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. In this context, the notation {8, 5, 2, 1} represents a set containing the numbers 8, 5, 2, and 1. Understanding set notation is crucial for determining whether a specific element, such as 9, belongs to the set.

Element Membership

Element membership refers to the relationship between an element and a set, denoted by the symbol '∈' for 'is an element of' and '∉' for 'is not an element of.' In the question, the statement '9 ∉ {8, 5, 2, 1}' asserts that 9 is not one of the elements in the specified set. Recognizing this relationship is essential for evaluating the truth of the statement.

True or False Statements

True or false statements are assertions that can be evaluated as either correct or incorrect. In mathematical logic, determining the truth value of a statement involves analyzing its components and their relationships. In this case, the statement about the membership of 9 in the set must be assessed to conclude whether it is true or false.