Let the universal set U be the set of all integers from 1 to 12 inclusive. Define A as the set of integers in U that are multiples of 3, and B as the set of integers in U that are multiples of 4. Which of the following sets represents the complement of the union of A and B, that is, (A ∪ B)'?
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Correct answer
A. {1, 2, 5, 7, 10, 11}
Principle or equation
The complement of a set S with respect to the universal set U is the set of all elements in U that are not in S. The union of sets A and B is the set of all elements that are in A or in B (or both).
Why this answer is correct
First list U = {1,2,3,4,5,6,7,8,9,10,11,12}. A = multiples of 3 = {3,6,9,12}. B = multiples of 4 = {4,8,12}. Then A ∪ B = {3,4,6,8,9,12}. The complement (A ∪ B)' consists of all integers from 1 to 12 not in that union: {1,2,5,7,10,11}.
Example
If U = {1,2,3,4,5}, A = {1,2}, B = {2,3}, then A ∪ B = {1,2,3} and (A ∪ B)' = {4,5}.
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