If U={1,2,3,4,5} and A=∅, what is A'?
Answer and explanation
Correct answer: {1,2,3,4,5}
The complement of A is defined relative to the universal set U: A'=U\A, or equivalently A'={x∈U : x∉A}. Since A is empty, none of the elements of U are removed. Consequently every element of U belongs to A', so A'=U={1,2,3,4,5}. The set {∅} is not the same as ∅, and 0 is not even an element of the given universal set.
Frequently asked questions
What is the correct answer to this question?
{1,2,3,4,5}
Why is this the correct answer?
The complement of A is defined relative to the universal set U: A'=U\A, or equivalently A'={x∈U : x∉A}. Since A is empty, none of the elements of U are removed. Consequently every element of U belongs to A', so A'=U={1,2,3,4,5}. The set {∅} is not the same as ∅, and 0 is not even an element of the given universal set.
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.
