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 47

Textbook Question

Determine whether each statement is true or false. {5, 8, 9} = {5, 8, 9, 0}

Verified step by step guidance

Identify the elements in each set. The first set contains elements {5, 8, 9} and the second set contains elements {5, 8, 9, 0}.

Compare the elements of the two sets. Check if every element in the first set is present in the second set and vice versa.

Notice that the element '0' is in the second set but not in the first set.

Recall the definition of set equality: Two sets are equal if and only if they contain exactly the same elements.

Conclude whether the statement '{5, 8, 9} = {5, 8, 9, 0}' is true or false based on the comparison and the definition of set equality.

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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.

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.

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.