If A = {x : x is a natural number}, B = {x : x is an even natural number}, C = {x : x is an odd natural number} and D = {x : x is a prime number}, find
A ∩ B
A ∩ B = {x : x is an even natural number} = B
A ∩ C
A ∩ C = {x : x is an odd natural number} = C
A ∩ D
A ∩ D = {x : x is a prime number} = D
B ∩ C
B ∩ C = ∅ (empty set)
B ∩ D
B ∩ D = {2}
C ∩ D
C ∩ D = {x : x is an odd prime number}
Explanation
This question tests understanding of set intersection and subset relationships. Since B (even natural numbers) and C (odd natural numbers) are both subsets of A (natural numbers), their intersections with A yield themselves. For B ∩ C, the result is empty because no number can be both even and odd simultaneously. For B ∩ D, the context explicitly states '2 is the only even prime number,' so the intersection is {2}. For C ∩ D, all prime numbers except 2 are odd, giving the set of odd primes.