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Reviewed CSCA Mathematics question · Hard

Let the universal set U be the set of all positive integers less than 25. Define A as the set of integers in U that are divisible by 4, and B as the set of integers in U that are divisible by 6. Which of the following sets is equal to A ∩ B' (the intersection of A with the complement of B in U)?

  1. {4, 8, 16, 20}
  2. {4, 8, 12, 16, 20, 24}
  3. {4, 8, 16, 20, 24}
  4. {4, 8, 12, 16, 20}
Show the answer and explanation

Correct answer

A. {4, 8, 16, 20}

Principle or equation

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

Why this answer is correct

U = {1,2,...,24}. A = {4,8,12,16,20,24}. B = {6,12,18,24}. B' = U \ B = {1,2,3,4,5,7,8,9,10,11,13,14,15,16,17,19,20,21,22,23}. Intersect A with B' gives {4,8,16,20}.

Example

If U = {1,2,3,4,5,6}, A = {2,4,6}, B = {3,6}, then B' = {1,2,4,5} and A ∩ B' = {2,4}.

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