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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1:13 minutes

Problem 64

Textbook Question

Insert ⊆ or s in each blank to make the resulting statement true. {1, 5} ____ {0, 1, 2, 3, 5}

Verified step by step guidance

Identify the relationship between the two sets: {1, 5} and {0, 1, 2, 3, 5}.

Check if every element of the first set {1, 5} is also an element of the second set {0, 1, 2, 3, 5}.

Since both 1 and 5 are present in the second set, {1, 5} is a subset of {0, 1, 2, 3, 5}.

Use the subset symbol \( \subseteq \) to indicate that {1, 5} is a subset of {0, 1, 2, 3, 5}.

The correct statement is: {1, 5} \( \subseteq \) {0, 1, 2, 3, 5}.

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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, sets are represented by curly braces, and elements are listed within them. Understanding how to read and write sets is crucial for determining relationships between them, such as subset and equality.

Subset

A subset is a set whose elements are all contained within another set. If set A is a subset of set B, denoted as A ⊆ B, every element of A is also an element of B. This concept is essential for comparing sets and understanding their relationships, particularly in the context of the given question.

Element of a Set

An element of a set is an individual object or number that belongs to that set. The notation 'a ∈ A' indicates that 'a' is an element of set A. Recognizing whether an element is part of a set is vital for determining the truth of statements involving sets, such as whether one set is a subset of another.