Use set-builder notation to write the set \( E \) of all odd natural numbers between 8 and 24 . Choose the correct set. A. \( E=\{8,9,10,11, \ldots, 23,24\} \) B. \( E=\{9,11,13, \ldots, 23\} \) C. \( E=\{x \mid x \in N \) and \( x \) is an odd number between 8 and 24\( \} \)

The correct representation of the set \( E \) of all odd natural numbers between 8 and 24 in set-builder notation is C. Here’s why: Set-builder notation allows you to describe a set by stipulating a property that its members must satisfy. In this case, the set \( E \) can be defined as the collection of all odd numbers \( x \) such that \( x \) is a natural number and lies within the bounds greater than 8 and less than 24. Thus, Option C \( E=\{x \mid x \in N \text{ and } x \text{ is an odd number between 8 and 24\} } \) captures this criterion perfectly! To illustrate the differences: - Option A lists all numbers between 8 and 24, including evens, which isn’t what we want. - Option B, while listing only odd numbers, doesn’t use set-builder notation and only shows specific examples rather than defining the set universally. So, it's all about finding the odd ducks (or in this case, numbers)! Happy math-ing!