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 32

Chapter 1, Problem 32

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

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: The element given is 0, and the set is $ \{0, 5, 6, 7, 8, 10\} $.

Check if the element 0 is listed inside the set: Look through the set to see if 0 appears as one of the elements.

Since 0 is found in the set $ \{0, 5, 6, 7, 8, 10\} $, the correct symbol to use is $ \in $.

Write the complete true statement: $ 0 \in \{0, 5, 6, 7, 8, 10\} $.

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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 object or number is an element of 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 belongs to a specified collection.

Notation of Sets

Sets are collections of distinct objects, often listed within curly braces {}. Each element inside the braces is a member of the set. Recognizing the elements listed helps in verifying membership and applying the correct symbol for inclusion or exclusion.

Use of Symbols ∈ and ∉

The symbols '∈' and '∉' are used to express membership relations between elements and sets. '∈' asserts that an element belongs to a set, while '∉' asserts it does not. Correct usage of these symbols is essential for accurately stating set membership.

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