If A′ ⊆ B′, which conclusion is always correct?
Answer and explanation
Correct answer: B ⊆ A
The complement operation reverses inclusion. Starting with A′ ⊆ B′ and taking complements of both sides gives (B′)′ ⊆ (A′)′, which simplifies to B ⊆ A. No equality or disjointness is forced by the given condition, so the other choices need not hold. Therefore, option A is the only conclusion that is always valid.
Frequently asked questions
What is the correct answer to this question?
B ⊆ A
Why is this the correct answer?
The complement operation reverses inclusion. Starting with A′ ⊆ B′ and taking complements of both sides gives (B′)′ ⊆ (A′)′, which simplifies to B ⊆ A. No equality or disjointness is forced by the given condition, so the other choices need not hold. Therefore, option A is the only conclusion that is always valid.
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.
