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 77

Textbook Question

Determine whether each statement is true or false. {1, 2, 4} ∪ {1, 2, 4} = {1, 2, 4}

Verified step by step guidance

Identify the operation: The problem involves the union of two sets.

Understand the union operation: The union of two sets combines all unique elements from both sets.

Examine the given sets: Both sets are {1, 2, 4}.

Perform the union: Combine the elements of both sets, ensuring no duplicates.

Compare the result: The union of {1, 2, 4} and {1, 2, 4} should be {1, 2, 4}.

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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. The union of sets A and B, denoted as A ∪ B, includes every element that is in A, in B, or in both. For example, if A = {1, 2} and B = {2, 3}, then A ∪ B = {1, 2, 3}. Understanding this concept is crucial for determining the truth of statements involving set operations.

Set Equality

Set equality occurs when two sets contain exactly the same elements, regardless of the order or repetition of those elements. For instance, the sets {1, 2, 4} and {4, 2, 1} are equal because they contain the same elements. This concept is essential for evaluating whether the result of a union operation matches a given set.

Element Membership

Element membership refers to whether a specific element is contained within a set. This is denoted by the symbol '∈', meaning 'is an element of'. For example, if we say 1 ∈ {1, 2, 4}, it indicates that 1 is indeed a member of the set. Understanding element membership helps in verifying the contents of sets when performing operations like union.