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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0:40 minutes

Problem 41

Textbook Question

Determine whether each statement is true or false. 1 ∈ {11, 5, 4, 3, 1}

Verified step by step guidance

Identify the set given in the problem: \( \{11, 5, 4, 3, 1\} \).

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

Check if the number 1 is listed as an element in the set \( \{11, 5, 4, 3, 1\} \).

Since 1 is present in the set, the statement '1 \in \{11, 5, 4, 3, 1\}' is true.

Conclude that the statement is true because 1 is indeed an element of 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. In this context, the curly braces {} indicate a set, and the elements within are the specific values included in that set. Understanding set notation is crucial for determining membership, which is the focus of the question.

Element Membership

Element membership refers to whether a specific item is included in a set. The symbol '∈' denotes that an element belongs to a set, while '∉' indicates it does not. In the question, we are asked to evaluate if the number 1 is an element of the set {11, 5, 4, 3, 1}, which requires checking the presence of 1 among the listed elements.

True or False Statements

True or false statements are assertions that can be evaluated for their validity. In mathematics, determining the truth value of a statement often involves logical reasoning and analysis of definitions. The question requires assessing the truth value of the membership statement regarding the number 1 and its inclusion in the specified set.