If x ∈ Aᶜ, which statement is correct?
Answer and explanation
Correct answer: x ∈ U and x ∉ A
By definition, the complement Aᶜ consists of the elements of the universal set U that are not in A. Therefore, the statement x ∈ Aᶜ means both x ∈ U and x ∉ A. Option A contradicts the definition, option C places x outside the universal set, and option D would require x to belong to both A and its complement, which is impossible.
Frequently asked questions
What is the correct answer to this question?
x ∈ U and x ∉ A
Why is this the correct answer?
By definition, the complement Aᶜ consists of the elements of the universal set U that are not in A. Therefore, the statement x ∈ Aᶜ means both x ∈ U and x ∉ A. Option A contradicts the definition, option C places x outside the universal set, and option D would require x to belong to both A and its complement, which is impossible.
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.
