If U = {1, 2, 3, 4, 5} is the universal set, what is U′?
Answer and explanation
Correct answer: ∅
The complement of a set contains the elements of the universal set that are not in that set. When the set itself is the universal set U, every element under consideration is already in U. There is therefore no element of U outside U. Consequently, U′ = U \ U = ∅. Option A is U itself, not its complement, while the singleton options omit several elements without justification.
Frequently asked questions
What is the correct answer to this question?
∅
Why is this the correct answer?
The complement of a set contains the elements of the universal set that are not in that set. When the set itself is the universal set U, every element under consideration is already in U. There is therefore no element of U outside U. Consequently, U′ = U \ U = ∅. Option A is U itself, not its complement, while the singleton options omit several elements without justification.
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.
