If A ∩ B′ = ∅, which conclusion is always true?
Answer and explanation
Correct answer: A ⊆ B
The condition A ∩ B′ = ∅ says that no element of A lies outside B. If an element x belongs to A, it cannot belong to B′, because that would place x in the empty intersection. Therefore x must belong to B. Since every element of A is in B, we conclude A ⊆ B. The other statements are stronger and need not hold, so option A is correct.
Frequently asked questions
What is the correct answer to this question?
A ⊆ B
Why is this the correct answer?
The condition A ∩ B′ = ∅ says that no element of A lies outside B. If an element x belongs to A, it cannot belong to B′, because that would place x in the empty intersection. Therefore x must belong to B. Since every element of A is in B, we conclude A ⊆ B. The other statements are stronger and need not hold, 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.
