Question - Set Theory Problem Involving Intersection of Sets in Roster Form

To find \( A \cap B \) in roster form, identify the elements common to both set \( A \) and set \( B \).

By definition from the question:

\( A = \{x: x \leq 10, x \in \mathbb{N}, x \text{ is a prime number}\} \)

\( B = \{x: x \in \mathbb{N}, x \text{ is even}\} \)

First list the prime numbers less than or equal to 10 (prime numbers are numbers greater than 1 that have no positive divisors other than 1 and itself): 2, 3, 5, 7

Now list the even natural numbers (since only 2 is both even and prime): 2

Therefore, the intersection of set A and set B, \( A \cap B \), which includes all the elements that are both prime and even is: {2}, since 2 is the only even prime number.

\( A \cap B = \{2\} \).