If A⊆B⊆C⊆U, then what is (A∪B∪C)′ equal to?
Answer and explanation
Correct answer: C′
The inclusions A⊆B and B⊆C show that every element of A and B is already an element of C. Therefore the union of the nested sets is the largest set: A∪B∪C=C. Taking the complement relative to the same universal set U gives (A∪B∪C)′=C′. The other complements are generally larger and need not equal the required set, while the empty set is not justified.
Frequently asked questions
What is the correct answer to this question?
C′
Why is this the correct answer?
The inclusions A⊆B and B⊆C show that every element of A and B is already an element of C. Therefore the union of the nested sets is the largest set: A∪B∪C=C. Taking the complement relative to the same universal set U gives (A∪B∪C)′=C′. The other complements are generally larger and need not equal the required set, while the empty set is not justified.
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.
