If A ⊆ U and A′ = U, what is A?
Answer and explanation
Correct answer: ∅
A′ contains the elements of U that are not in A. If A′ equals the whole universal set U, then every element of U is outside A. Consequently, A contains no elements and must be the empty set: A = ∅. This also follows from the complement identity ∅′ = U. Option A would imply A′ = ∅, not U; option C is not a value for A, and option D is incorrect because the condition determines A uniquely.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
A′ contains the elements of U that are not in A. If A′ equals the whole universal set U, then every element of U is outside A. Consequently, A contains no elements and must be the empty set: A = ∅. This also follows from the complement identity ∅′ = U. Option A would imply A′ = ∅, not U; option C is not a value for A, and option D is incorrect because the condition determines A uniquely.
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.
