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 5, and B as the set of integers in U that are multiples of 7. Which of the following sets is equal to A' ∩ B?
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Correct answer
A. {7, 14}
Principle or equation
The complement of A (A') consists of all elements in U that are not in A. The intersection A' ∩ B consists of all elements that are in both A' and B.
Why this answer is correct
U = {1,2,...,20}. A = {5,10,15,20}. B = {7,14}. A' = {1,2,3,4,6,7,8,9,11,12,13,14,16,17,18,19}. Intersecting A' with B gives {7,14}.
Example
If U = {1,2,3,4,5}, A = {2,4}, B = {1,2,3}, then A' = {1,3,5} and A' ∩ B = {1,3}.
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