If Aᶜ ⊆ Bᶜ, which of the following conclusions is correct?
Answer and explanation
Correct answer: B ⊆ A
For complements taken with respect to the same universal set, inclusion reverses when complements are taken. The statement Aᶜ ⊆ Bᶜ can be viewed as Yᶜ ⊆ Xᶜ, which implies X ⊆ Y in reverse notation; hence B ⊆ A. The original inclusion A ⊆ B is not logically forced, and neither equality nor disjointness follows from the given condition.
Frequently asked questions
What is the correct answer to this question?
B ⊆ A
Why is this the correct answer?
For complements taken with respect to the same universal set, inclusion reverses when complements are taken. The statement Aᶜ ⊆ Bᶜ can be viewed as Yᶜ ⊆ Xᶜ, which implies X ⊆ Y in reverse notation; hence B ⊆ A. The original inclusion A ⊆ B is not logically forced, and neither equality nor disjointness follows from the given condition.
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.
