If A ⊆ U, then A′ is a subset of which set?
Answer and explanation
Correct answer: U
The complement of A is defined with respect to U: A′ = U − A = {x ∈ U : x ∉ A}. Every element of A′ therefore comes from the universal set U, so A′ ⊆ U. It is not generally a subset of A, because A and A′ are disjoint. P(A) is the collection of subsets of A, not the natural containing set for A′, and the complement need not be empty. Thus option B is correct.
Frequently asked questions
What is the correct answer to this question?
U
Why is this the correct answer?
The complement of A is defined with respect to U: A′ = U − A = {x ∈ U : x ∉ A}. Every element of A′ therefore comes from the universal set U, so A′ ⊆ U. It is not generally a subset of A, because A and A′ are disjoint. P(A) is the collection of subsets of A, not the natural containing set for A′, and the complement need not be empty. Thus option B 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.
