Questions: Express the set in roster form. B=x x ∈ W ∩ x ≤ 3 (A) B=0.1,2, (B) B=4,5,6, ... C It is impossible to write this in roster form because it is an infinite number of numbers (D) B=0.1,2,3 (E) B=1,2,3

Express the set in roster form.
B=x x ∈ W ∩ x ≤ 3
(A) B=0.1,2,
(B) B=4,5,6, ...
C It is impossible to write this in roster form because it is an infinite number of numbers
(D) B=0.1,2,3
(E) B=1,2,3

Transcript text: Express the set in roster form. \[ \mathrm{B}=\{x \mid x \in W \cap x \leq 3\} \] (A) $B=\{0.1,2$, (B) $B=\{4,5,6, \ldots\}$ C It is impossible to write this in roster form because it is an infinite number of numbers (D) $B=\{0.1,2,3\}$ (E) $B=\{1,2,3\}$

Solution

Solution Steps

To express the set $ B $ in roster form, we need to identify all elements $ x $ that belong to the set of whole numbers $ W $ and are less than or equal to 3. Whole numbers are non-negative integers (0, 1, 2, 3, ...). Therefore, we need to list all whole numbers that are less than or equal to 3.

Step 1: Identify the Set of Whole Numbers

Whole numbers ($ W $) are non-negative integers: $ 0, 1, 2, 3, \ldots $.

Step 2: Apply the Condition $ x \leq 3 $

We need to find all whole numbers $ x $ such that $ x \leq 3 $.

Step 3: List the Elements

The whole numbers that satisfy $ x \leq 3 $ are $ 0, 1, 2, $ and $ 3 $.