If A ⊆ B, which relation is correct for their complements?
Answer and explanation
Correct answer: Bᶜ ⊆ Aᶜ
When A is a subset of B, every element of A is also an element of B. Taking complements reverses the inclusion order: an element outside B is certainly outside A, because A is contained in B. Hence every element of Bᶜ belongs to Aᶜ, and Bᶜ ⊆ Aᶜ. Equality is not guaranteed unless A and B are equal. The intersection in option D is also not generally the universal set.
Frequently asked questions
What is the correct answer to this question?
Bᶜ ⊆ Aᶜ
Why is this the correct answer?
When A is a subset of B, every element of A is also an element of B. Taking complements reverses the inclusion order: an element outside B is certainly outside A, because A is contained in B. Hence every element of Bᶜ belongs to Aᶜ, and Bᶜ ⊆ Aᶜ. Equality is not guaranteed unless A and B are equal. The intersection in option D is also not generally the universal set.
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.
