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

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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:
   $$
   \textbf{D. } \{x \in \mathbb{N} \mid 13 < x < 18\}
   $$
The correct set builder notation is $$ \{x \in \mathbb{N} \mid 13 < x < 18\} $$.

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

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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