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 4, and B as the set of integers in U that are divisible by 6. Which of the following sets is equal to the complement of A union B, that is (A ∪ B)'?
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Correct answer
A. {1, 2, 3, 5, 7, 9, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 27, 29}
Principle or equation
The complement of a set consists of all elements in the universal set that are not in the set. The union of two sets contains all elements that belong to at least one of the sets.
Why this answer is correct
First list all integers from 1 to 29. A = {4, 8, 12, 16, 20, 24, 28}. B = {6, 12, 18, 24}. A ∪ B = {4, 6, 8, 12, 16, 18, 20, 24, 28}. The complement consists of all numbers in U not in A ∪ B: {1, 2, 3, 5, 7, 9, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 25, 26, 27, 29}.
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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