If U = {p, q, r} and A = ∅, what is A′, the complement of A with respect to U?
Answer and explanation
Correct answer: A′ = U = {p, q, r} (पूरक is the universal set)
The complement A′ of a set A contains all elements of the universal set U that do not belong to A. Here A is the empty set, so it contains no elements at all. Consequently, none of the elements p, q, or r is excluded from the complement. Every element of U therefore belongs to A′, giving A′ = U = {p, q, r}. This illustrates the standard identity ∅′ = U.
Frequently asked questions
What is the correct answer to this question?
A′ = U = {p, q, r} (पूरक is the universal set)
Why is this the correct answer?
The complement A′ of a set A contains all elements of the universal set U that do not belong to A. Here A is the empty set, so it contains no elements at all. Consequently, none of the elements p, q, or r is excluded from the complement. Every element of U therefore belongs to A′, giving A′ = U = {p, q, r}. This illustrates the standard identity ∅′ = 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.
