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