If |U| = 20, |A| = 12, |B| = 9, and |A ∩ B| = 5, what is |(A ∪ B)'|?
Answer and explanation
Correct answer: 4
Use the inclusion–exclusion formula: |A ∪ B| = |A| + |B| − |A ∩ B|. Therefore, |A ∪ B| = 12 + 9 − 5 = 16. The complement contains the elements of U that are not in A ∪ B, so |(A ∪ B)'| = |U| − |A ∪ B| = 20 − 16 = 4. Hence, option B is correct. Subtracting the intersection is essential because common elements would otherwise be counted twice.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
Use the inclusion–exclusion formula: |A ∪ B| = |A| + |B| − |A ∩ B|. Therefore, |A ∪ B| = 12 + 9 − 5 = 16. The complement contains the elements of U that are not in A ∪ B, so |(A ∪ B)'| = |U| − |A ∪ B| = 20 − 16 = 4. Hence, option B is correct. Subtracting the intersection is essential because common elements would otherwise be counted twice.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
