Express the set using set-builder notation. Use inequality notation to express the condition $x$ must meet in order to be a member of the set. \[ \{58,59,60,61, \ldots, 82\} \] Choose the correct answer below. A. $\{x \mid x \in N$ and $x \geq 58\}$ B. $\{x \mid x \in N$ and $58 \leq x \leq 61$ and $x=82\}$ c. $\{x \mid x \in N$ and $58 \leq x \leq 82\}$ D. $\{x \in N$ and $58 \leq x \leq 82\}$

Step 1 ：Express the set using set-builder notation. Use inequality notation to express the condition $x$ must meet in order to be a member of the set. The set is \(\{58,59,60,61, \ldots, 82\}\).

Step 2 ：Choose the correct answer below. A. \(\{x \mid x \in N \text{ and } x \geq 58\}\) B. \(\{x \mid x \in N \text{ and } 58 \leq x \leq 61 \text{ and } x=82\}\) C. \(\{x \mid x \in N \text{ and } 58 \leq x \leq 82\}\) D. \(\{x \in N \text{ and } 58 \leq x \leq 82\}\)

Step 3 ：The set contains all natural numbers from 58 to 82 inclusive. Therefore, the set-builder notation should reflect this. The correct notation should be \(\{x \mid x \in N \text{ and } 58 \leq x \leq 82\}\). This means that $x$ is a member of the set if $x$ is a natural number and $x$ is greater than or equal to 58 and less than or equal to 82.

Step 4 ：Final Answer: The correct answer is \(\boxed{\{x \mid x \in N \text{ and } 58 \leq x \leq 82\}}\).