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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0:37 minutes

Problem 39

Textbook Question

Determine whether each statement is true or false. 3 ∈ {2, 5, 6, 8}

Verified step by step guidance

Understand the symbol \( \in \), which means 'is an element of'.

Identify the set given in the problem: \( \{2, 5, 6, 8\} \).

Check if the number 3 is listed as one of the elements in the set.

Since 3 is not listed among the elements \( \{2, 5, 6, 8\} \), determine the truth value of the statement.

Conclude whether the statement '3 \( \in \) \{2, 5, 6, 8\}' is true or false based on your findings.

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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 {2, 5, 6, 8} represents a set containing the numbers 2, 5, 6, and 8. Understanding set notation is crucial for determining membership, which indicates whether a specific element belongs to a given set.

Element Membership

Element membership refers to the relationship between an element and a set, denoted by the symbol '∈'. If an element is part of a set, we say it is a member of that set. For example, in the statement 3 ∈ {2, 5, 6, 8}, we need to assess whether the number 3 is included in the specified set to determine the truth value of the statement.

True or False Statements

True or false statements are logical assertions that can be evaluated as either true or false. In mathematics, determining the truth value of a statement often involves checking conditions or relationships, such as membership in a set. Understanding how to evaluate these statements is essential for logical reasoning and problem-solving in algebra.