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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1:16 minutes

Problem 46

Textbook Question

Determine whether each statement is true or false. {3, 0, 9, 6, 2} = {2, 9, 0, 3, 6}

Verified step by step guidance

Identify the elements in the first set: \{3, 0, 9, 6, 2\}.

Identify the elements in the second set: \{2, 9, 0, 3, 6\}.

Recall that sets are collections of distinct objects where order does not matter.

Compare the elements of both sets to see if they contain the same elements.

Conclude whether the sets are equal based on the comparison of their elements.

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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 in which those elements are listed. For example, the sets {1, 2, 3} and {3, 2, 1} are equal because they contain the same elements.

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}, as the duplicate '1' is disregarded. This principle is crucial for determining set equality.

Order of Elements in Sets

The order of elements in a set does not affect its identity. This means that the arrangement of elements is irrelevant when comparing sets. For example, {a, b} is the same set as {b, a}, which is essential for evaluating the equality of two sets.