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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1:21 minutes

Problem 65

Textbook Question

Insert ⊆ or s in each blank to make the resulting statement true. {0, 1, 2} ____ {1, 2, 3, 4, 5}

Verified step by step guidance

Identify the symbols: The symbol '⊆' represents 'is a subset of', meaning all elements of the first set are contained within the second set. The symbol 's' is not standard in set theory.

Examine the first set {0, 1, 2} and the second set {1, 2, 3, 4, 5}.

Check if every element of the first set {0, 1, 2} is also an element of the second set {1, 2, 3, 4, 5}.

Notice that the element '0' from the first set is not present in the second set.

Conclude that the first set is not a subset of the second set, so the correct symbol to use is neither '⊆' nor 's'.

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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 symbols ⊆ (subset) and s (not a subset) are used to express relationships between sets. Understanding how to interpret these symbols is crucial for determining whether one set is contained within another.

Subset Definition

A subset is defined as a set where every element of the first set is also an element of the second set. For example, if A = {0, 1, 2} and B = {1, 2, 3, 4, 5}, A is a subset of B if all elements of A are found in B. This concept is essential for evaluating the relationship between the two sets in the question.

Element Inclusion

Element inclusion refers to the presence of specific elements from one set in another set. In the given example, we need to check if all elements of the set {0, 1, 2} are included in the set {1, 2, 3, 4, 5}. Understanding this relationship helps in deciding whether to use the subset symbol ⊆ or the non-subset symbol s.