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

Previous problemNext problem

1:22 minutes

Problem 45

Textbook Question

Determine whether each statement is true or false. {2, 5, 8, 9} = {2, 5, 9, 8}

Verified step by step guidance

Identify the elements in each set. The first set is \{2, 5, 8, 9\} and the second set is \{2, 5, 9, 8\}.

Recall that in set theory, the order of elements in a set does not matter. Sets are defined by their elements, not the order of those elements.

Compare the elements of both sets. Check if both sets contain the same elements.

Verify that each element in the first set is present in the second set and vice versa.

Conclude that if both sets contain exactly the same elements, then the statement is true. Otherwise, it is false.>

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above

Video duration:

Play a video:

Was this helpful?

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 set theory, each element in a set is unique, meaning that duplicates are not counted. For instance, the set {2, 2, 5} is equivalent to the set {2, 5} because the repeated element does not affect the overall composition of the set.

Order of Elements

The order of elements in a set does not matter. This means that the arrangement of elements does not influence the identity of the set. For example, the sets {a, b} and {b, a} are the same set, as they contain the same elements.