If A ⊆ B and B′ ⊆ C, which statement about A′ is always true?
Answer and explanation
Correct answer: B′ ⊆ A′
Set inclusion reverses when complements are taken. From A ⊆ B, every element of A is in B, so any element outside B must also be outside A. Therefore B′ ⊆ A′. The condition B′ ⊆ C is additional information but is not needed for this conclusion. Hence option A is always true, while the other options need not hold.
Frequently asked questions
What is the correct answer to this question?
B′ ⊆ A′
Why is this the correct answer?
Set inclusion reverses when complements are taken. From A ⊆ B, every element of A is in B, so any element outside B must also be outside A. Therefore B′ ⊆ A′. The condition B′ ⊆ C is additional information but is not needed for this conclusion. Hence option A is always true, while the other options need not hold.
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.
