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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1:11 minutes

Problem 36

Textbook Question

Insert ∈ or ∉ in each blank to make the resulting statement true. {2} ____ {2, 4, 6, 8}

Verified step by step guidance

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

Examine the set on the right side of the blank: {2, 4, 6, 8}.

Determine if the element on the left side of the blank, which is {2}, is present in the set on the right.

Since {2} is a set containing the number 2, check if this set itself is an element of the set {2, 4, 6, 8}.

Conclude that {2} is not an element of {2, 4, 6, 8}, so the correct symbol to use is ∉.

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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 sets. In this context, the set {2, 4, 6, 8} contains the elements 2, 4, 6, and 8. Understanding how to read and interpret set notation is essential for determining relationships between individual elements and sets.

Element of a Set

The concept of an element of a set refers to whether a specific item belongs to a given set. The symbol '∈' indicates that an element is a member of a set, while '∉' indicates that it is not. For example, since 2 is included in the set {2, 4, 6, 8}, the correct symbol to use in this case would be '∈'.

Logical Statements

Logical statements are assertions that can be evaluated as true or false. In this question, the task is to determine the truth value of the statement involving the element 2 and the set {2, 4, 6, 8}. Understanding how to construct and evaluate these statements is crucial for correctly filling in the blanks with the appropriate symbols.