1. The problem is about understanding the sets \(A\) and \(B\).\n\n2. Set \(A = \{x: x \text{ is an odd natural number}\}\) includes all positive integers that are odd, such as 1, 3, 5, 7, 9, ...\n\n3. Set \(B = \{x: x \text{ is a prime number}\}\) includes all natural numbers greater than 1 that have no positive divisors other than 1 and itself, such as 2, 3, 5, 7, 11, ...\n\n4. An interesting observation is the intersection \(A \cap B\) is the set of odd prime numbers since all prime numbers except 2 are odd. This includes numbers like 3, 5, 7, 11, 13, ...\n\n5. The union \(A \cup B\) is the set of all numbers that are either odd natural numbers or prime numbers. This includes all odd natural numbers plus the prime number 2.\n\n6. Set \(A\) is infinite as there are infinitely many odd natural numbers. Similarly, set \(B\) is infinite because there are infinitely many prime numbers.