If A ⊆ B ⊆ U, what can be said about B′ ⊆ A′?
Answer and explanation
Correct answer: It is always true
Taking complements reverses the direction of set inclusion. Since every element of A is also in B, any element that is outside B must certainly be outside A. Thus every element of B′ belongs to A′, which proves B′ ⊆ A′. This is called the order-reversing property of complements. The statement does not require A = U or B = ∅, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
It is always true
Why is this the correct answer?
Taking complements reverses the direction of set inclusion. Since every element of A is also in B, any element that is outside B must certainly be outside A. Thus every element of B′ belongs to A′, which proves B′ ⊆ A′. This is called the order-reversing property of complements. The statement does not require A = U or B = ∅, so 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.
