Let the universal set U be the set of all positive integers less than 30. Define A as the set of integers in U that are divisible by 3, and B as the set of integers in U that are divisible by 5. Which of the following sets is equal to A ∩ B' (the intersection of A and the complement of B)?
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Correct answer
A. {3, 6, 9, 12, 18, 21, 24, 27}
Principle or equation
The complement of B in U consists of elements in U not divisible by 5. A ∩ B' is the set of multiples of 3 less than 30 that are not multiples of 5.
Why this answer is correct
U = {1,2,...,29}. A = {3,6,9,12,15,18,21,24,27}. B = {5,10,15,20,25}. B' = U \ B. A ∩ B' removes 15 from A, leaving {3,6,9,12,18,21,24,27}.
Example
If U = {1,...,10}, A = multiples of 2, B = multiples of 3, then A ∩ B' = {2,4,8,10}.
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