If A ⊆ B and B ⊆ U, why is B′ ⊆ A′ true?
Answer and explanation
Correct answer: A larger set gives a smaller complement
If A is a subset of B, every element of A is also in B. Consequently, an element that is outside B cannot be in A; otherwise it would be in B as well. Therefore every element of B′ is an element of A′, which proves B′ ⊆ A′. Taking complements reverses the direction of inclusion. Option A expresses this correctly: the larger set B leaves a smaller complement, while the smaller set A leaves a larger complement.
Frequently asked questions
What is the correct answer to this question?
A larger set gives a smaller complement
Why is this the correct answer?
If A is a subset of B, every element of A is also in B. Consequently, an element that is outside B cannot be in A; otherwise it would be in B as well. Therefore every element of B′ is an element of A′, which proves B′ ⊆ A′. Taking complements reverses the direction of inclusion. Option A expresses this correctly: the larger set B leaves a smaller complement, while the smaller set A leaves a larger complement.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
