If A ⊆ U and A′ = U, what must A be?
Answer and explanation
Correct answer: A = ∅
The complement A′ contains all elements of U that are not members of A. If A′ equals the whole universal set U, then every element of U lies outside A. Therefore A contains no elements and must be the empty set, A = ∅. If A were U, its complement would be empty, not U. The statement A = A′ is not generally implied, and A ≠ ∅ directly contradicts the condition.
Frequently asked questions
What is the correct answer to this question?
A = ∅
Why is this the correct answer?
The complement A′ contains all elements of U that are not members of A. If A′ equals the whole universal set U, then every element of U lies outside A. Therefore A contains no elements and must be the empty set, A = ∅. If A were U, its complement would be empty, not U. The statement A = A′ is not generally implied, and A ≠ ∅ directly contradicts the condition.
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.
