If U = {1, 2, 3, 4, 5} and A′ = {2, 5}, what is A ∩ A′?
Answer and explanation
Correct answer: ∅
A′ contains precisely the elements of U that are not in A. Therefore A and A′ are disjoint: an element cannot simultaneously belong to A and to its complement. This gives the fundamental identity A ∩ A′ = ∅, regardless of the particular elements in U or A′. In this question A′ = {2, 5}, so 2 and 5 are outside A, and no common element exists. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
A′ contains precisely the elements of U that are not in A. Therefore A and A′ are disjoint: an element cannot simultaneously belong to A and to its complement. This gives the fundamental identity A ∩ A′ = ∅, regardless of the particular elements in U or A′. In this question A′ = {2, 5}, so 2 and 5 are outside A, and no common element exists. Hence 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.
