Write the set in set builder notation. \( \{14,15,16,17\} \) A. \( \{x \in N \mid 14

Ask by Blake Schwartz. in the United States

Mar 18,2025

1. We start with the set \( \{14, 15, 16, 17\} \). 2. The goal is to use set builder notation to express all the elements of the set. In other words, we need a condition that exactly picks the natural numbers \(14, 15, 16,\) and \(17\). 3. Option D is \[ \{x \in \mathbb{N} \mid 13 < x < 18\} \] We check the inequality: - If \(x = 14\), then \(13 < 14 < 18\) holds. - If \(x = 15\), then \(13 < 15 < 18\) holds. - If \(x = 16\), then \(13 < 16 < 18\) holds. - If \(x = 17\), then \(13 < 17 < 18\) holds. 4. No number outside \(\{14, 15, 16, 17\}\) satisfies \(13 < x < 18\) when \(x\) is a natural number. 5. Therefore, the correct answer is: \[ \textbf{D. } \{x \in \mathbb{N} \mid 13 < x < 18\} \]