If |U| = 80, |A| = 35, |B| = 40, and |A ∩ B| = 15, what is |(A ∪ B)ᶜ|?
Advertisement
Answer and explanation
Correct answer: 20
Use the inclusion-exclusion formula: |A ∪ B| = |A| + |B| − |A ∩ B|. Substituting the given values gives |A ∪ B| = 35 + 40 − 15 = 60. The complement contains all elements of U outside this union, so |(A ∪ B)ᶜ| = |U| − |A ∪ B| = 80 − 60 = 20. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
20
Why is this the correct answer?
Use the inclusion-exclusion formula: |A ∪ B| = |A| + |B| − |A ∩ B|. Substituting the given values gives |A ∪ B| = 35 + 40 − 15 = 60. The complement contains all elements of U outside this union, so |(A ∪ B)ᶜ| = |U| − |A ∪ B| = 80 − 60 = 20. Therefore option A is correct.
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.
Advertisement