Suppose A and B are subsets of the same universal set. If Bᶜ ⊆ Aᶜ, which conclusion is correct?
Answer and explanation
Correct answer: A ⊆ B
Complementation reverses the direction of inclusion. In general, if X ⊆ Y, then Yᶜ ⊆ Xᶜ; conversely, if Yᶜ ⊆ Xᶜ, then X ⊆ Y. Applying this converse rule to Bᶜ ⊆ Aᶜ gives A ⊆ B. The statement B ⊆ A reverses the result incorrectly, while A = Bᶜ and A ∩ B = ∅ are stronger claims that do not necessarily follow from the given information. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
A ⊆ B
Why is this the correct answer?
Complementation reverses the direction of inclusion. In general, if X ⊆ Y, then Yᶜ ⊆ Xᶜ; conversely, if Yᶜ ⊆ Xᶜ, then X ⊆ Y. Applying this converse rule to Bᶜ ⊆ Aᶜ gives A ⊆ B. The statement B ⊆ A reverses the result incorrectly, while A = Bᶜ and A ∩ B = ∅ are stronger claims that do not necessarily follow from the given information. Hence option A 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.
