Write the following sets in the roster form :
B={x|x=2n, n `in` W and `n lt5`}

Answer

To write the set B in roster form, we will follow these steps:

### Step 1: Understand the definition of the set
The set B is defined as:
\[ B = \{ x | x = 2n, n \in W \text{ and } n < 5 \} \]
Here, \( W \) represents the set of whole numbers, which are \( 0, 1, 2, 3, 4, \ldots \)

### Step 2: Identify the values of n
Since \( n \) is a whole number and must be less than 5, the possible values of \( n \) are:
\[ n = 0, 1, 2, 3, 4 \]

### Step 3: Calculate the corresponding values of x
Now, we will substitute each value of \( n \) into the equation \( x = 2n \) to find the corresponding values of \( x \):

- For \( n = 0 \):
\[ x = 2 \times 0 = 0 \]

- For \( n = 1 \):
\[ x = 2 \times 1 = 2 \]

- For \( n = 2 \):
\[ x = 2 \times 2 = 4 \]

- For \( n = 3 \):
\[ x = 2 \times 3 = 6 \]

- For \( n = 4 \):
\[ x = 2 \times 4 = 8 \]

### Step 4: Write the set in roster form
Now, we can compile all the values of \( x \) we calculated:
\[ B = \{ 0, 2, 4, 6, 8 \} \]

### Final Answer
Thus, the set B in roster form is:
\[ B = \{ 0, 2, 4, 6, 8 \} \]

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