Question

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. (63, 64, 65, 66, …) choose the correct answer below. a. {x | x∈n and 63≤x≤66} b. {x | x∈n and x≥63} c. {x∈n and x≥63} d. {x | x≥63}

Explanation:

Step1: Analyze the given set

The set is $\{63, 64, 65, 66, ...\}$, which includes all natural numbers starting at 63 and continuing infinitely.

Step2: Evaluate each option

• Option A: $\{x \mid x\in\mathbb{N} \text{ and } 63\leq x\leq 66\}$ only includes numbers up to 66, which does not match the infinite set.
• Option B: $\{x \mid x\in\mathbb{N} \text{ and } x\geq 63\}$ correctly identifies the set as all natural numbers $x$ where $x$ is greater than or equal to 63, matching the given set.
• Option C: $\{x\in\mathbb{N} \text{ and } x\geq 63\}$ uses incorrect set-builder notation (missing the vertical bar separator).
• Option D: $\{x \mid x\geq 63\}$ does not specify that $x$ must be a natural number, so it would include non-integer values like 63.5, which are not in the original set.

Answer:

B. $\{x \mid x\in\mathbb{N} \text{ and } x\geq 63\}$