Write each of the following sets in Roster form and write the cardinal number of each .
B = {x : x ` in N , 3x- 6 lt 9} `

Answer

To solve the problem, we need to express the set B in roster form and find its cardinal number.

### Step-by-Step Solution:

1. **Understand the Set Definition**:
The set B is defined as:
\[ B = \{ x : x \in \mathbb{N}, 3x - 6 < 9 \} \]
This means we are looking for natural numbers \( x \) that satisfy the inequality \( 3x - 6 < 9 \).

2. **Solve the Inequality**:
Start by isolating \( x \) in the inequality:
\[ 3x - 6 < 9 \]
Add 6 to both sides:
\[ 3x < 9 + 6 \]
Simplifying gives:
\[ 3x < 15 \]
Now, divide both sides by 3:
\[ x < 5 \]

3. **Identify Natural Numbers**:
Since \( x \) must be a natural number (which starts from 1), we find the natural numbers less than 5:
\[ x = 1, 2, 3, 4 \]

4. **Write in Roster Form**:
The set B in roster form is:
\[ B = \{ 1, 2, 3, 4 \} \]

5. **Find the Cardinal Number**:
The cardinal number of a set is the count of distinct elements in that set. Here, the elements are 1, 2, 3, and 4. Therefore, the cardinal number is:
\[ |B| = 4 \]

### Final Answer:
The set B in roster form is:
\[ B = \{ 1, 2, 3, 4 \} \]
The cardinal number of set B is:
\[ |B| = 4 \]

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