Classify the following sets as empty set finite set or infinite set :
the set of even prime numbers

Answer

To classify the set of even prime numbers, we will follow these steps:

### Step-by-Step Solution:

1. **Define Even Numbers**:
Even numbers are integers that can be divided by 2 without leaving a remainder. Examples include 0, 2, 4, 6, 8, etc.

**Hint**: Remember that even numbers are multiples of 2.

2. **Define Prime Numbers**:
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. Examples include 2, 3, 5, 7, 11, etc.

**Hint**: A prime number must be greater than 1 and cannot be divided evenly by any other numbers except for 1 and itself.

3. **Identify Even Prime Numbers**:
Now, we need to find numbers that are both even and prime. The only even prime number is 2. All other even numbers can be divided by 2, which means they have at least three divisors (1, 2, and the number itself), making them non-prime.

**Hint**: Think about the definition of prime numbers and check if any even number other than 2 fits that definition.

4. **Count the Even Prime Numbers**:
Since we have identified that the only even prime number is 2, we can conclude that there is only one element in this set.

**Hint**: Count how many numbers you have identified in the set.

5. **Classify the Set**:
A set with a finite number of elements is called a finite set. Since we have only one element (2), the set of even prime numbers is a finite set.

**Hint**: Recall the definitions of finite sets (countable) and infinite sets (uncountable).

### Final Answer:
The set of even prime numbers is a **finite set**.