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Use set-builder notation to write the set \( E \) of all odd natural numbers between 6 and 20 . Choose the correct set. A. \( E=\{x \mid x \in N \) and \( x \) is an odd number between 6 and 20\( \} \) B. \( E=\{6,7,8,9, \ldots, 19,20\} \) C. \( E=\{7,9,11, \ldots, 19\} \)

Ask by Bright Simmons. in the United States
Mar 16,2025

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Answer

The correct set in set-builder notation is \( E = \{ x \in \mathbb{N} \mid x \text{ is odd and } 6 < x < 20 \} \).

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Beyond the Answer

The correct set is A. In set-builder notation, we define the set \( E \) as \( E = \{ x \mid x \in \mathbb{N} \text{ and } x \text{ is an odd number between 6 and 20} \} \). It captures exactly the odd natural numbers within the specified range, highlighting the conditions for inclusion. To clarify with a sneak peek into the definition of odd and natural numbers, natural numbers start from 1 and go on infinitely (1, 2, 3, ...), while odd numbers are those that cannot be divided evenly by 2 (like 1, 3, 5, ...). So, within the range of 6 to 20, the odd natural numbers are 7, 9, 11, 13, 15, 17, and 19—just the right fits for our set \( E \)!

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