Use the definition below to select the statement that is false. A = {xEZ: x is even and 4 < x < 17} 4¢ A 6 € A 17 A |A| = 7

Algebra and Trigonometry (6th Edition)
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Instructions:**

Use the definition below to select the statement that is false.

\[ A = \{ x \in \mathbb{Z} : x \text{ is even and } 4 < x < 17 \} \]

**Options:**

- ○ \( 4 \notin A \)
- ○ \( 6 \in A \)
- ○ \( 17 \notin A \)
- ○ \(|A| = 7\)

**Explanation:**

The set \( A \) consists of even integers \( x \) such that \( 4 < x < 17 \). This means the elements of \( A \) are the even numbers 6, 8, 10, 12, 14, and 16. There are 6 elements in set \( A \). The false statement is \(|A| = 7\), as the correct number of elements is 6.
Transcribed Image Text:**Instructions:** Use the definition below to select the statement that is false. \[ A = \{ x \in \mathbb{Z} : x \text{ is even and } 4 < x < 17 \} \] **Options:** - ○ \( 4 \notin A \) - ○ \( 6 \in A \) - ○ \( 17 \notin A \) - ○ \(|A| = 7\) **Explanation:** The set \( A \) consists of even integers \( x \) such that \( 4 < x < 17 \). This means the elements of \( A \) are the even numbers 6, 8, 10, 12, 14, and 16. There are 6 elements in set \( A \). The false statement is \(|A| = 7\), as the correct number of elements is 6.
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