If P is a set of all prime factors of 30 and Q is a set of all factors of 18 less than 10, find P $\cap$ Q

Step 1: Analyze the question We need the set P of prime factors of 30, the set Q of factors of 18 that are less than 10, and then their intersection (the elements that appear in both sets).

Step 2: Find P 30 = 2 × 3 × 5 So P = {2, 3, 5}

Step 3: Find Q Factors of 18: 1, 2, 3, 6, 9, 18 Those less than 10: 1, 2, 3, 6, 9 So Q = {1, 2, 3, 6, 9}

Step 4: Find P ∩ Q Elements common to both sets:

• 2 is in P and in Q ✓
• 3 is in P and in Q ✓
• 5 is in P but not in Q ✗

So P ∩ Q = {2, 3}

Answer: B

Exam tip: "Prime factors" means only the prime numbers that divide the number, so 1 is never included. "Factors" includes 1 and the number itself. Always list each set fully before finding the intersection, and remember that ∩ means "in both" while ∪ means "in either".