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A= (1, 2, (3, 4), (5, 6, 7}} Select the statement that is true. {3} € A {3,4} CA {1,2} CA {1,2} € A

A= (1, 2, (3, 4), (5, 6, 7}} Select the statement that is true. {3} € A {3,4} CA {1,2} CA {1,2} € A

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
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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**Problem Statement:** Given the set \( A = \{1, 2, \{3, 4\}, \{5, 6, 7\}\} \), select the statement that is true. 1. \( \{3\} \in A \) 2. \( \{3, 4\} \subseteq A \) 3. \( \{1, 2\} \subseteq A \) 4. \( \{1, 2\} \in A \) **Solution:** - Statement 1: \( \{3\} \in A \) - False, because \( \{3\} \) is not an element of \( A \). \( A \) contains the set \( \{3, 4\} \), not \( \{3\} \). - Statement 2: \( \{3, 4\} \subseteq A \) - False, because \( \{3, 4\} \) is an element of \( A \), not a subset of \( A \). - Statement 3: \( \{1, 2\} \subseteq A \) - True, because both 1 and 2 are individual elements of \( A \). - Statement 4: \( \{1, 2\} \in A \) - False, because the set \( \{1, 2\} \) is not an element of \( A \); rather, 1 and 2 are separate elements. Thus, the correct statement is: **\( \{1, 2\} \subseteq A \)**.
Transcribed Image Text:**Problem Statement:** Given the set \( A = \{1, 2, \{3, 4\}, \{5, 6, 7\}\} \), select the statement that is true. 1. \( \{3\} \in A \) 2. \( \{3, 4\} \subseteq A \) 3. \( \{1, 2\} \subseteq A \) 4. \( \{1, 2\} \in A \) **Solution:** - Statement 1: \( \{3\} \in A \) - False, because \( \{3\} \) is not an element of \( A \). \( A \) contains the set \( \{3, 4\} \), not \( \{3\} \). - Statement 2: \( \{3, 4\} \subseteq A \) - False, because \( \{3, 4\} \) is an element of \( A \), not a subset of \( A \). - Statement 3: \( \{1, 2\} \subseteq A \) - True, because both 1 and 2 are individual elements of \( A \). - Statement 4: \( \{1, 2\} \in A \) - False, because the set \( \{1, 2\} \) is not an element of \( A \); rather, 1 and 2 are separate elements. Thus, the correct statement is: **\( \{1, 2\} \subseteq A \)**.
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