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Reviewed CSCA Mathematics question · Hard

Let the universal set U be the set of all integers from 1 to 18 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 is equal to (A ∪ B)′ (the complement of the union of A and B)?

  1. {1, 2, 5, 7, 10, 11, 13, 14, 17}
  2. {1, 2, 5, 7, 10, 11, 13, 14, 17, 18}
  3. {1, 2, 5, 7, 10, 11, 13, 14, 16, 17}
  4. {1, 2, 5, 7, 10, 11, 13, 14, 17, 19}
Show the answer and explanation

Correct answer

A. {1, 2, 5, 7, 10, 11, 13, 14, 17}

Principle or equation

The complement of a set S with respect to U is the set of all elements in U that are not in S. (A ∪ B)′ consists of elements in U that are neither multiples of 3 nor multiples of 4.

Why this answer is correct

First list U = {1,2,...,18}. A = {3,6,9,12,15,18}, B = {4,8,12,16}. Then A ∪ B = {3,4,6,8,9,12,15,16,18}. The complement in U is {1,2,5,7,10,11,13,14,17}.

Example

If U = {1,2,3,4,5} and A = {2,4}, then A′ = {1,3,5}.

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