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Reviewed CSCA Mathematics question · Standard

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 2, and B as the set of integers in U that are multiples of 3. Which of the following sets is equal to A ∩ B' (the intersection of A with the complement of B)?

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

Correct answer

A. {2, 4, 8, 10}

Principle or equation

The complement of B in U is the set of elements in U not in B. The intersection of A and B' is the set of elements that are in A and not in B.

Why this answer is correct

U = {1,2,3,4,5,6,7,8,9,10,11,12}. A = {2,4,6,8,10,12}. B = {3,6,9,12}. B' = {1,2,4,5,7,8,10,11}. A ∩ B' = {2,4,8,10}.

Example

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

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