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 represents the complement of the union of A and B?
Show the answer and explanation
Correct answer
A. {1, 2, 3, 5, 7, 9, 10, 11, 13, 14, 15}
Principle or equation
The complement of a set S with respect to universal set U is the set of all elements in U that are not in S. Here S = A ∪ B, so we need all integers from 1 to 15 that are neither multiples of 4 nor multiples of 6.
Why this answer is correct
First list U = {1,2,3,4,5,6,7,8,9,10,11,12,13,14,15}. A = {4,8,12} (multiples of 4). B = {6,12} (multiples of 6). A ∪ B = {4,6,8,12}. The complement in U is {1,2,3,5,7,9,10,11,13,14,15}.
Example
If U = {1,2,3,4,5} and C = {2,4}, then C' = {1,3,5}.
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