If A ⊆ U, B ⊆ U, and A ⊆ B, which relation is correct for their complements?
Answer and explanation
Correct answer: B′ ⊆ A′
Since A is a subset of B, every element of A is also an element of B. Therefore, an element that is not in B cannot be in A. The complement B′ contains all elements of the universal set U that are outside B, while A′ contains all elements outside A. Hence every element of B′ is also in A′, so B′ ⊆ A′. This is the reversal property of complementation.
Frequently asked questions
What is the correct answer to this question?
B′ ⊆ A′
Why is this the correct answer?
Since A is a subset of B, every element of A is also an element of B. Therefore, an element that is not in B cannot be in A. The complement B′ contains all elements of the universal set U that are outside B, while A′ contains all elements outside A. Hence every element of B′ is also in A′, so B′ ⊆ A′. This is the reversal property of complementation.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Power Set and Subsets.
