Table of contents
- 0. Review of Algebra4h 16m
- 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 19m
- 10. Combinatorics & Probability1h 45m
0. Review of Algebra
Exponents
1:21 minutes
Problem 47b
Textbook Question
Textbook QuestionDetermine whether each statement is true or false. {5, 8, 9} = {5, 8, 9, 0}
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Set Equality
Set equality states that two sets are considered equal if they contain exactly the same elements, regardless of the order or the number of times elements appear. For example, the sets {1, 2, 3} and {3, 2, 1} are equal because they contain the same elements. In the given question, we need to compare the elements of both sets to determine if they are equal.
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Element Uniqueness in Sets
In set theory, each element in a set is unique, meaning that duplicates are not counted. For instance, the set {1, 1, 2} is equivalent to the set {1, 2}. This concept is crucial when evaluating the equality of sets, as it affects how we interpret the contents of each set in the question.
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Empty Set
The empty set, denoted as {}, is a set that contains no elements. It is a fundamental concept in set theory and is considered a subset of every set. In the context of the question, the presence of the empty set in the second set {5, 8, 9, 0} does not affect the equality with the first set {5, 8, 9}, as the empty set does not contribute any elements.
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