Let the universal set U be the set of all integers from 1 to 15 inclusive. Define A as the set of integers in U that are multiples of 4, and B as the set of integers in U that are multiples of 6. Which of the following sets is equal to A ∩ B' (the intersection of A with the complement of B)?
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Correct answer
B. {4, 8}
Principle or equation
The complement of B (B') consists of all elements in the universal set that are not in B. The intersection A ∩ B' includes elements that are in A and also in B'.
Why this answer is correct
U = {1, 2, ..., 15}. A = {4, 8, 12} (multiples of 4 up to 15). B = {6, 12} (multiples of 6 up to 15). B' = U \ B = {1, 2, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15}. Intersection A ∩ B' = {4, 8} because 12 is in B and thus not in B'.
Example
If U = {1,2,3,4,5}, A = {2,4}, B = {3,4}, then B' = {1,2,5}, A ∩ B' = {2}.
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