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If P = {x: x is even, x ≤ 10, x ∈ N} and Q = {x: x is prime, x ≤ 10, x ∈ N}, then P ∩ Q is ________.

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Final answer:

The intersection of the sets P (even numbers ≤ 10) and Q (prime numbers ≤ 10) is the single number 2, as it is the only number that is both even and prime.

Step-by-step explanation:

The sets P = {x: x is even, x ≤ 10, x ∈ N} and Q = {x: x is prime, x ≤ 10, x ∈ N} consist of numbers under 10 from the set of natural numbers that satisfy specific properties. The set P includes the even numbers which are ≤ 10 (2, 4, 6, 8, 10), while the set Q includes the prime numbers which are ≤ 10 (2, 3, 5, 7). The intersection of P and Q, denoted as P ∩ Q, includes all the elements that are both even and prime. In this case, the only number that is even and prime is 2, making it the sole member of P ∩ Q.

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