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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0:45 minutes

Problem 31

Textbook Question

Insert ∈ or ∉ in each blank to make the resulting statement true. 0 _____ {0, 2, 3, 4}

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Identify the meaning of the symbols: ∈ means 'is an element of' and ∉ means 'is not an element of'.

Examine the set given: \( \{0, 2, 3, 4\} \).

Determine if the number 0 is listed within the set \( \{0, 2, 3, 4\} \).

Since 0 is present in the set, the correct symbol to use is ∈.

Insert the symbol: 0 ∈ \{0, 2, 3, 4\}.

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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 language used to describe collections of objects, known as elements. In this context, the set {0, 2, 3, 4} contains specific numbers, and we use symbols like ∈ (element of) and ∉ (not an element of) to indicate whether a particular number is included in the set.

Element Membership

Element membership refers to the relationship between an element and a set. If an element is part of a set, we denote this with the symbol ∈. Conversely, if the element is not part of the set, we use ∉. Understanding this concept is crucial for determining the correct symbol to use in the given statement.

Understanding the Set

To solve the problem, one must analyze the set {0, 2, 3, 4} to see if the number 0 is included. Since 0 is explicitly listed as an element of the set, the correct symbol to use in the blank is ∈, indicating that 0 is indeed a member of the set.