`B={y : 2y+1 lt 3 " and " y in W}`

Answer

To solve the problem step by step, we will follow the instructions given in the video transcript.

### Step 1: Understand the Set Notation
The set \( B \) is defined as:
\[ B = \{ y : 2y + 1 < 3 \text{ and } y \in W \} \]
where \( W \) represents the set of whole numbers.

### Step 2: Solve the Inequality
We need to solve the inequality \( 2y + 1 < 3 \).

1. Start with the inequality:
\[ 2y + 1 < 3 \]

2. Subtract 1 from both sides:
\[ 2y < 3 - 1 \]
\[ 2y < 2 \]

3. Divide both sides by 2:
\[ y < 1 \]

### Step 3: Identify Whole Numbers Less Than 1
Since we are looking for whole numbers (non-negative integers), we need to find which whole numbers are less than 1. The whole numbers are \( 0, 1, 2, 3, \ldots \).

The only whole number that is less than 1 is:
- \( 0 \)

### Step 4: Write the Set in Rooster Form
Now that we have identified the only whole number that satisfies the condition, we can write the set \( B \) in roster form:
\[ B = \{ 0 \} \]

### Final Answer
Thus, the set \( B \) is:
\[ B = \{ 0 \} \]

---