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Reviewed CSCA Mathematics question · Hard

Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} be the universal set. Define A = {1, 2, 3, 4, 5} and B = {2, 4, 6, 8}. Which of the following sets is equal to (A ∪ B) ∩ (A' ∪ B)?

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

Correct answer

A. {2, 4, 6, 8}

Principle or equation

Set operations: union (∪), intersection (∩), and complement (') with respect to the universal set U.

Why this answer is correct

First, find A ∪ B = {1,2,3,4,5,6,8}. The complement of A is A' = {6,7,8,9,10}. Then A' ∪ B = {2,4,6,7,8,9,10}. The intersection of {1,2,3,4,5,6,8} and {2,4,6,7,8,9,10} is {2,4,6,8}, which is exactly B.

Example

For U={1,2,3}, A={1}, B={2}, then (A∪B)∩(A'∪B) = {1,2}∩{2,3} = {2} = B.

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