If A ⊆ B, which relation is always correct?
Answer and explanation
Correct answer: Bᶜ ⊆ Aᶜ
If every element of A is also an element of B, then any element outside B must certainly be outside A. Therefore the complement of B is contained in the complement of A: Bᶜ ⊆ Aᶜ. This reversal of inclusion is called the complement or order-reversing property. The other statements are not generally true because A and B may be unequal and need not exhaust U.
Frequently asked questions
What is the correct answer to this question?
Bᶜ ⊆ Aᶜ
Why is this the correct answer?
If every element of A is also an element of B, then any element outside B must certainly be outside A. Therefore the complement of B is contained in the complement of A: Bᶜ ⊆ Aᶜ. This reversal of inclusion is called the complement or order-reversing property. The other statements are not generally true because A and B may be unequal and need not exhaust U.
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.
