Let the universal set U be the set of all integers from 1 to 20 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)'?
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Correct answer
A. {1, 2, 3, 5, 7, 9, 10, 11, 13, 14, 15, 17, 19}
Principle or equation
The complement of a set A ∪ B consists of all elements in the universal set U that are not in A ∪ B. A ∪ B contains all multiples of 4 or 6 within U.
Why this answer is correct
First list A = {4, 8, 12, 16, 20} and B = {6, 12, 18}. Then A ∪ B = {4, 6, 8, 12, 16, 18, 20}. The complement in U = {1, 2, 3, ..., 20} is {1, 2, 3, 5, 7, 9, 10, 11, 13, 14, 15, 17, 19}.
Example
If U = {1,2,3,4,5}, A = {2,4}, B = {3}, then A ∪ B = {2,3,4} and (A ∪ B)' = {1,5}.
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