Write each of the following sets in Roster form:
D = set of all composite numbers between 23 and 33.

Answer

To write the set D in roster form, we need to identify all the composite numbers between 23 and 33. Let's go through the steps one by one.

### Step 1: Understand Composite Numbers
Composite numbers are natural numbers greater than 1 that are not prime. This means they have more than two distinct positive divisors.

### Step 2: Identify the Range
We need to find composite numbers between 23 and 33. This means we will consider the numbers 24, 25, 26, 27, 28, 29, 30, 31, and 32.

### Step 3: Check Each Number
Now, we will check each number in this range to see if it is composite:

- **24**: Divisors are 1, 2, 3, 4, 6, 8, 12, 24 (Composite)
- **25**: Divisors are 1, 5, 25 (Composite)
- **26**: Divisors are 1, 2, 13, 26 (Composite)
- **27**: Divisors are 1, 3, 9, 27 (Composite)
- **28**: Divisors are 1, 2, 4, 7, 14, 28 (Composite)
- **29**: Divisors are 1, 29 (Prime)
- **30**: Divisors are 1, 2, 3, 5, 6, 10, 15, 30 (Composite)
- **31**: Divisors are 1, 31 (Prime)
- **32**: Divisors are 1, 2, 4, 8, 16, 32 (Composite)

### Step 4: List the Composite Numbers
From our checks, the composite numbers between 23 and 33 are:
- 24
- 25
- 26
- 27
- 28
- 30
- 32

### Step 5: Write in Roster Form
Now we can write the set D in roster form:
\[ D = \{ 24, 25, 26, 27, 28, 30, 32 \} \]

### Final Answer
Thus, the set of all composite numbers between 23 and 33 in roster form is:
\[ D = \{ 24, 25, 26, 27, 28, 30, 32 \} \]

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