`B={p : p in W " and " p^(2) lt 20}`

Answer

To find the set \( B \) defined as \( B = \{ p : p \in W \text{ and } p^2 < 20 \} \), where \( W \) is the set of whole numbers, we will follow these steps:

### Step 1: Understand the condition
We need to find whole numbers \( p \) such that \( p^2 < 20 \).

### Step 2: Identify whole numbers
Whole numbers start from 0 and go upwards: \( 0, 1, 2, 3, 4, 5, \ldots \)

### Step 3: Calculate \( p^2 \) for each whole number
- For \( p = 0 \):
\[ p^2 = 0^2 = 0 \quad (\text{which is less than } 20) \]
- For \( p = 1 \):
\[ p^2 = 1^2 = 1 \quad (\text{which is less than } 20) \]
- For \( p = 2 \):
\[ p^2 = 2^2 = 4 \quad (\text{which is less than } 20) \]
- For \( p = 3 \):
\[ p^2 = 3^2 = 9 \quad (\text{which is less than } 20) \]
- For \( p = 4 \):
\[ p^2 = 4^2 = 16 \quad (\text{which is less than } 20) \]
- For \( p = 5 \):
\[ p^2 = 5^2 = 25 \quad (\text{which is greater than } 20) \]

### Step 4: Determine the valid values of \( p \)
From the calculations, the values of \( p \) that satisfy \( p^2 < 20 \) are \( 0, 1, 2, 3, \) and \( 4 \).

### Step 5: Write the set \( B \)
Thus, the set \( B \) is:
\[ B = \{ 0, 1, 2, 3, 4 \} \]

### Final Answer
The set \( B \) is \( \{ 0, 1, 2, 3, 4 \} \).

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