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 29

Chapter 1, Problem 29

Insert ∈ or ∉ in each blank to make the resulting statement true. 5 ____ {4, 6, 8, 10}

Verified step by step guidance

Understand the problem: We need to determine whether the number 5 is an element of the set \{4, 6, 8, 10\} or not. The symbols used are \( \in \) meaning "is an element of" and \( \notin \) meaning "is not an element of".

Look at the set \( \{4, 6, 8, 10\} \) and identify its elements. The set contains the numbers 4, 6, 8, and 10.

Check if the number 5 is listed among the elements of the set. Since 5 is not in the list \(4, 6, 8, 10\), it is not an element of the set.

Based on this, choose the correct symbol to complete the statement: since 5 is not in the set, use \( \notin \).

Write the complete true statement as: \(5 \notin \{4, 6, 8, 10\}\).

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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 specific element belongs to a given set. The symbol '∈' denotes that an element is a member of the set, meaning it is included within the set's elements.

Set Notation and Symbols

Set notation uses curly braces {} to list elements, and symbols like '∈' (element of) and '∉' (not an element of) to express membership. Understanding these symbols is essential to correctly interpret and complete statements about sets.

Evaluating Membership in a Set

To determine if an element belongs to a set, compare the element to the listed members. If the element matches any member, it belongs (∈); if not, it does not belong (∉). This evaluation is key to correctly filling in the blank.

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