If A ⊆ U and A′ = ∅, what is the correct conclusion?
Answer and explanation
Correct answer: A = U
The complement A′ consists of all elements of the universal set U that are not in A. If A′ = ∅, there is no element of U outside A. Since A is already a subset of U, it must contain every element of U. Therefore, A = U. The condition does not imply that either set is empty; it means A covers the whole universal set.
Frequently asked questions
What is the correct answer to this question?
A = U
Why is this the correct answer?
The complement A′ consists of all elements of the universal set U that are not in A. If A′ = ∅, there is no element of U outside A. Since A is already a subset of U, it must contain every element of U. Therefore, A = U. The condition does not imply that either set is empty; it means A covers the whole universal set.
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.
