Which pair of sets is always disjoint?
Answer and explanation
Correct answer: A and Aᶜ
A set and its complement contain mutually exclusive elements: an element cannot belong to A and not belong to A at the same time. Hence their intersection is always empty, A ∩ Aᶜ = ∅, so A and Aᶜ are always disjoint. The other pairs need not be disjoint because A and U, Aᶜ and U, or U and U generally share elements.
Frequently asked questions
What is the correct answer to this question?
A and Aᶜ
Why is this the correct answer?
A set and its complement contain mutually exclusive elements: an element cannot belong to A and not belong to A at the same time. Hence their intersection is always empty, A ∩ Aᶜ = ∅, so A and Aᶜ are always disjoint. The other pairs need not be disjoint because A and U, Aᶜ and U, or U and U generally share elements.
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.
