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Reviewed CSCA Mathematics question · Standard

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 3, and B as the set of integers in U that are multiples of 5. Which of the following sets represents the complement of the intersection of A and B, denoted (A ∩ B)'?

  1. {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15}
  2. {1, 2, 4, 5, 7, 8, 10, 11, 13, 14}
  3. {1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14}
  4. {1, 2, 4, 6, 7, 8, 9, 11, 12, 13, 14}
Show the answer and explanation

Correct answer

C. {1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14}

Principle or equation

The complement of a set is the set of all elements in the universal set that are not in the given set. The intersection of two sets contains elements that belong to both sets.

Why this answer is correct

First find A = {3, 6, 9, 12, 15} and B = {5, 10, 15}. Their intersection is A ∩ B = {15}. The complement of this set in U is all elements of U except 15, which is {1, 2, 3, 4, 6, 7, 8, 9, 11, 12, 13, 14}.

Example

For U = {1, 2, 3, 4, 5}, A = {2, 4}, B = {3, 4}, then A ∩ B = {4} and (A ∩ B)' = {1, 2, 3, 5}.

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