Write each of the following sets in Roster form and write the cardinal number of each .
D = ` {x: x in W, x- 3 lt 2 }.`

Answer

To solve the problem, we need to write the set \( D \) in roster form and find its cardinal number. Here’s how we can do that step by step:

### Step 1: Understand the set notation
The set \( D \) is defined as:
\[ D = \{ x : x \in W, x - 3 < 2 \} \]
This means we are looking for elements \( x \) that are whole numbers (denoted by \( W \)) and satisfy the condition \( x - 3 < 2 \).

### Step 2: Solve the inequality
We start with the inequality:
\[ x - 3 < 2 \]
To isolate \( x \), we add 3 to both sides:
\[ x < 5 \]

### Step 3: Identify the whole numbers less than 5
Since \( x \) must be a whole number, we list all whole numbers that are less than 5:
- Whole numbers are \( 0, 1, 2, 3, 4, \ldots \)
- The whole numbers less than 5 are \( 0, 1, 2, 3, 4 \).

### Step 4: Write the set in roster form
Thus, we can write the set \( D \) in roster form as:
\[ D = \{ 0, 1, 2, 3, 4 \} \]

### Step 5: Find the cardinal number
The cardinal number of a set is the number of elements in that set. In this case, we count the elements in \( D \):
- The elements are \( 0, 1, 2, 3, 4 \), which gives us a total of 5 elements.

Therefore, the cardinal number of the set \( D \) is:
\[ |D| = 5 \]

### Final Answer
The set in roster form is:
\[ D = \{ 0, 1, 2, 3, 4 \} \]
And the cardinal number is:
\[ |D| = 5 \]