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Reviewed CSCA Mathematics question · Hard

Let the universal set U be the set of all positive integers less than 20. Define A as the set of integers in U that are divisible by 2, and B as the set of integers in U that are divisible by 3. Which of the following sets is equal to A ∩ B' (the intersection of A and the complement of B)?

  1. {2, 4, 8, 10, 14, 16}
  2. {2, 4, 6, 8, 10, 12, 14, 16, 18}
  3. {2, 4, 8, 10, 14, 16, 20}
  4. {1, 5, 7, 11, 13, 17, 19}
Show the answer and explanation

Correct answer

A. {2, 4, 8, 10, 14, 16}

Principle or equation

The complement of B consists of elements in U not in B. The intersection A ∩ B' consists of elements that are in A and not in B.

Why this answer is correct

U = {1,2,...,19}. A = {2,4,6,8,10,12,14,16,18}. B = {3,6,9,12,15,18}. B' = {1,2,4,5,7,8,10,11,13,14,16,17,19}. Intersection with A gives {2,4,8,10,14,16}.

Example

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

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