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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1:35 minutes

Problem 76

Textbook Question

Determine whether each statement is true or false. {3, 5, 9, 10} ∪ ∅ = {3, 5, 9, 10}

Verified step by step guidance

Identify the union operation symbol (∪) which combines all unique elements from both sets involved.

Recognize that the empty set (∅) contains no elements.

Understand that combining any set with the empty set will not add any new elements to the original set.

Apply the union operation to the sets {3, 5, 9, 10} and ∅.

Conclude that since the empty set adds no elements to the other set, the result of the union is just the original set {3, 5, 9, 10}.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Set Union

Set union is an operation that combines all unique elements from two or more sets. When performing a union, if an element appears in any of the sets, it will be included in the resulting set. For example, the union of {1, 2} and {2, 3} is {1, 2, 3}.

Empty Set

The empty set, denoted as ∅, is a set that contains no elements. It is a fundamental concept in set theory, serving as the identity element for the union operation. When any set is united with the empty set, the result is the original set itself.

Set Equality

Two sets are considered equal if they contain exactly the same elements, regardless of the order or repetition of those elements. For instance, {1, 2, 3} is equal to {3, 2, 1}. Understanding set equality is crucial for determining the truth of statements involving sets.