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Let A denote the set of all divisors of 15, B the set of prime numbers less than 10, and C the set of even numbers less than 9. Then the set (A ∪ C) ∩ B is

1. {1, 3, 5}
2. {1, 2, 3}
3. {2, 3, 5}
4. {2, 5}

Correct answer: {2, 3, 5}

Solution

The correct option includes the elements that are both in the union of the divisors of 15 and the even numbers less than 9, and also in the set of prime numbers less than 10. The divisors of 15 are {1, 3, 5, 15}, and the even numbers less than 9 are {0, 2, 4, 6, 8}. The union of these sets is {1, 2, 3, 4, 5, 6, 8, 15}, and the intersection with the prime numbers less than 10, which are {2, 3, 5, 7}, results in {2, 3, 5}.

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