Write the following sets in roster form and also in set builder form :
the set of prime numbers less than 25

Answer

To solve the problem of writing the set of prime numbers less than 25 in both roster form and set builder form, we will follow these steps:

### Step 1: Identify Prime Numbers Less Than 25
Prime numbers are numbers greater than 1 that have no divisors other than 1 and themselves. We need to find all the prime numbers that are less than 25.

**Prime numbers less than 25 are:**
- 2
- 3
- 5
- 7
- 11
- 13
- 17
- 19
- 23

### Step 2: Write the Set in Roster Form
In roster form, we list all the elements of the set within curly braces.

**Roster Form:**
Let \( A \) be the set of prime numbers less than 25. Thus, we can write:
\[ A = \{ 2, 3, 5, 7, 11, 13, 17, 19, 23 \} \]

### Step 3: Write the Set in Set Builder Form
In set builder form, we describe the set by stating the property that its members satisfy.

**Set Builder Form:**
We can express the set \( A \) as:
\[ A = \{ x \mid x \text{ is a prime number and } x < 25 \} \]

### Final Answer
- **Roster Form:** \( A = \{ 2, 3, 5, 7, 11, 13, 17, 19, 23 \} \)
- **Set Builder Form:** \( A = \{ x \mid x \text{ is a prime number and } x < 25 \} \)

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