If the universal set U = {1, 2, 3, 4} and A = U, what is A′, the complement of A?
Answer and explanation
Correct answer: ∅
The complement A′ consists of elements of U that are not in A. Since A is equal to the entire universal set U, every element of U already belongs to A, so there are no elements left outside A. Using the rule A′ = U − A, we obtain A′ = U − U = ∅. Hence option C is correct. The set {0} cannot be the answer because 0 is not in U.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
The complement A′ consists of elements of U that are not in A. Since A is equal to the entire universal set U, every element of U already belongs to A, so there are no elements left outside A. Using the rule A′ = U − A, we obtain A′ = U − U = ∅. Hence option C is correct. The set {0} cannot be the answer because 0 is not in 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.
