Write the following sets in the roster form :
F = {x:x `in` N, `15ltxlt50` and x is divisible by 6}

Answer

To write the set F in roster form, we need to follow these steps:

### Step 1: Understand the conditions
The set F is defined as:
- \( x \) belongs to the natural numbers (N)
- \( 15 < x < 50 \)
- \( x \) is divisible by 6

### Step 2: Identify the range of numbers
We need to find natural numbers that are greater than 15 and less than 50. The natural numbers in this range are:
- 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49

### Step 3: Find numbers divisible by 6
Next, we need to find which of these numbers are divisible by 6. A number is divisible by 6 if it is divisible by both 2 and 3. We can check each number in the range:
- 18 (divisible by 6)
- 24 (divisible by 6)
- 30 (divisible by 6)
- 36 (divisible by 6)
- 42 (divisible by 6)
- 48 (divisible by 6)

### Step 4: List the numbers in roster form
The numbers that satisfy all the conditions are:
- 18, 24, 30, 36, 42, 48

Thus, the set F in roster form is:
\[ F = \{ 18, 24, 30, 36, 42, 48 \} \]