If A = ∅ and the universal set is U, what is A' equal to?
Answer and explanation
Correct answer: U
The complement A' is defined as the set of all elements in the universal set U that are not in A. If A is the empty set, it contains no elements, so no element of U is removed. Consequently every element of U belongs to A', and therefore ∅' = U. Option A confuses a set with its complement, while P(U) is a different power set.
Frequently asked questions
What is the correct answer to this question?
U
Why is this the correct answer?
The complement A' is defined as the set of all elements in the universal set U that are not in A. If A is the empty set, it contains no elements, so no element of U is removed. Consequently every element of U belongs to A', and therefore ∅' = U. Option A confuses a set with its complement, while P(U) is a different power set.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, Finite and Infinite Sets, Equal Sets.
