Ch. R - Review of Basic Concepts

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. R - Review of Basic Concepts

Problem 31

Chapter 1, Problem 31

Insert ∈ or ∉ in each blank to make the resulting statement true. 0 _____ {0, 2, 3, 4}

Verified step by step guidance

Understand the symbols: The symbol $ \in $ means "is an element of," and $ \notin $ means "is not an element of."

Identify the element and the set: Here, the element is 0, and the set is $ \{0, 2, 3, 4\} $.

Check if the element is in the set: Look at the set $ \{0, 2, 3, 4\} $ and see if 0 is listed as one of its members.

Since 0 is listed in the set, the correct symbol to use is $ \in $, meaning 0 is an element of the set.

Write the complete true statement: $ 0 \in \{0, 2, 3, 4\} $.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Set Membership (Element of a Set)

Set membership refers to whether a particular element belongs to a given set. The symbol '∈' means 'is an element of,' indicating inclusion, while '∉' means 'is not an element of,' indicating exclusion. Understanding this helps determine if a number is contained within a set.

Notation of Sets

Sets are collections of distinct objects, often listed within curly braces {}. Each item inside the braces is an element of the set. Recognizing the elements listed helps in identifying membership and performing operations involving sets.

Numbers and Their Classification

Understanding the nature of numbers, such as integers and their values, is essential to determine if a specific number is part of a set. For example, knowing that 0 is an integer and checking if it appears in the set {0, 2, 3, 4} is crucial for correct membership assignment.

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Insert ∈ or ∉ in each blank to make the resulting statement true. 0 _____ {0, 5, 6, 7, 8, 10}

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If the expression is in exponential form, write it in radical form and evaluate if possible. If it is in radical form, write it in exponential form. Assume all variables represent positive real numbers. ⁵√ k²

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Find each product. $x^{2} (3 x - 2) (5 x + 1)$

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Multiply or divide as indicated. Write answers in lowest terms as needed. (21/8)∙(4/7)