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(c) Write \( \left\{x \in U \mid x=n^{2}\right. \) for some \( \left.n \in N\right\} \) by listing the elements in braces. Choose the correct answer below. A. \( \{1,4,9,16\} \) B. C. \( \{1,2,3,4\} \) D. \( \{2,3,5,7,8,10,11,12,13,14,15,17,18,19,20\} \)

Ask by Barrett Hammond. in the United States
Mar 17,2025

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Answer

The correct answer is \( \{1, 4, 9, 16\} \), which is option A.

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Mind Expander

The set \( \{x \in U \mid x=n^{2} \text{ for some } n \in N\} \) consists of perfect squares. If \( N \) represents the natural numbers (1, 2, 3, ...), the corresponding perfect squares will be \( 1^2, 2^2, 3^2, 4^2, \) and so on. As we list these for \( n=1, 2, 3, \) and \( 4 \), we get \( \{1, 4, 9, 16\} \). So the correct answer is: A. \( \{1, 4, 9, 16\} \)

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