Question

express the set using the roster method. {x | x∈n and x ≤ 6} choose the correct answer below. a. {1, 2, 3, 4, 5, 6} b. {1, 2, 3, 4, 5} c. {0, 1, 2, 3, 4, 5, 6} d. {…, -3, -2, -1, 0, 1, 2, 3, 4, 5}

Explanation:

Step1: Define natural numbers $\mathbb{N}$

Typically, $\mathbb{N}$ includes non-negative integers: $0,1,2,3,...$

Step2: Filter numbers ≤6

Select all $x \in \mathbb{N}$ where $x \leq 6$: $0,1,2,3,4,5,6$

Step3: Write in roster form

Enclose the numbers in curly braces.

Answer:

C. {0, 1, 2, 3, 4, 5, 6}