If the universal set μ = {x : 1 ≤ x ≤ 20} and A = {y : multiple of 3} B = |z : odd numbers} Find A ∩ B

Analyze the question: We need A ∩ B, the elements that are in both A and B, with everything restricted to the universal set μ = {1, 2, 3, ..., 20}.

Concept: The intersection (∩) of two sets contains only the elements common to both sets.

Solution:

1. Universal set: μ = {1, 2, 3, ..., 20}

2. A = multiples of 3 in μ: A = {3, 6, 9, 12, 15, 18}

3. B = odd numbers in μ: B = {1, 3, 5, 7, 9, 11, 13, 15, 17, 19}

4. Elements found in both A and B: • 3 is in both ✓ • 6 is even ✗ • 9 is in both ✓ • 12 is even ✗ • 15 is in both ✓ • 18 is even ✗

A ∩ B = {3, 9, 15}

Checking the options:

• A. {1, 3, 6}: 1 is not a multiple of 3, and 6 is not odd. ✗
• B. {3, 5, 9, 12}: 5 is not a multiple of 3, and 12 is not odd. ✗
• C. {3, 9, 15}: all are odd multiples of 3. ✓
• D. {2, 3, 9}: 2 is neither odd nor a multiple of 3, and 15 is missing. ✗

Tip: Odd multiples of 3 follow the pattern 3, 9, 15, 21, ... (add 6 each time). Here you stop at 20, so you get 3, 9, 15. Whenever you see "multiples of a number" and "odd/even", just list both sets and circle the common elements.