If A ⊆ B ⊆ U, which of the following is always true?
Answer and explanation
Correct answer: Bᶜ ⊆ Aᶜ
Since A is a subset of B, every element of A is also in B. Taking complements with respect to the same universal set reverses the direction of inclusion: if X ⊆ Y, then Yᶜ ⊆ Xᶜ. Therefore, A ⊆ B implies Bᶜ ⊆ Aᶜ. Equality is not guaranteed unless A and B are equal, and the other options contradict complement laws.
Frequently asked questions
What is the correct answer to this question?
Bᶜ ⊆ Aᶜ
Why is this the correct answer?
Since A is a subset of B, every element of A is also in B. Taking complements with respect to the same universal set reverses the direction of inclusion: if X ⊆ Y, then Yᶜ ⊆ Xᶜ. Therefore, A ⊆ B implies Bᶜ ⊆ Aᶜ. Equality is not guaranteed unless A and B are equal, and the other options contradict complement laws.
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.
