How many elements are sets of even prime numbers?

A. One

B. Two

C. Three

D. Four

To determine how many elements are in the set of even prime numbers, we first need to understand what prime numbers are and then identify which of them are even.

Defining Prime Numbers

A prime number is defined as a natural number greater than 1 that has no positive divisors other than 1 and itself. This means that a prime number can only be divided evenly (without a remainder) by 1 and the number itself.

Identifying Even Numbers

Even numbers are integers that can be divided by 2 without leaving a remainder. The general form of an even number is 2n, where n is an integer. The smallest even number is 2, and all other even numbers can be generated by adding 2 repeatedly to 2.

Combining the Concepts

Now, let's look for even numbers that are also prime. The only even prime number is 2. This is because:

• 2 is divisible by 1 and 2, meeting the criteria for being prime.
• All other even numbers (like 4, 6, 8, etc.) can be divided by 2, which means they have at least one additional divisor besides 1 and themselves, thus disqualifying them from being prime.

Conclusion on the Set of Even Prime Numbers

Since 2 is the only number that fits both criteria of being even and prime, the set of even prime numbers contains just one element. Therefore, the answer to your question is:

A. One