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. $$ E=\{7,9,11, \ldots, 19\} $$

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1. We first identify the odd natural numbers between 6 and 20. The odd numbers in this interval are 
   $$
   7, 9, 11, 13, 15, 17, 19.
   $$

2. In set-builder notation, we want to describe the set $$ E $$ as all $$ x $$ in the natural numbers $$ \mathbb{N} $$ that are odd and satisfy $$ 6 < x < 20 $$. One way to write this is:
   $$
   E = \{ x \in \mathbb{N} \mid x \text{ is odd and } 6 < x < 20 \}.
   $$

3. Comparing the choices:
   - **Choice A:** $$ E=\{x \mid x \in N \text{ and } x \text{ is an odd number between 6 and 20}\} $$ correctly expresses this idea.
   - **Choice B:** Lists all numbers between 6 and 20 without specifying odd numbers.
   - **Choice C:** Enumerates the correct odd numbers, but it is not in set-builder notation.

4. Thus, the correct set in set-builder notation is given by **Choice A**.
The correct set in set-builder notation is $$ E = \{ x \in \mathbb{N} \mid x \text{ is odd and } 6 < x < 20 \} $$.

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. \( E=\{7,9,11, \ldots, 19\} \)

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