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Reviewed CSCA Mathematics question · Easy

Let the universal set U be the set of all integers from 1 to 10 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}
  3. {1, 3, 5, 7, 9}
  4. {3, 6, 9}
Show the answer and explanation

Correct answer

A. {2, 4, 8, 10}

Principle or equation

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

Why this answer is correct

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

Example

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

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