If 4 ∈ Aᶜ, which statement is correct?
Answer and explanation
Correct answer: 4 ∈ U and 4 ∉ A
Membership in the complement Aᶜ means that the element is part of the universal set U but is excluded from A. Therefore, from 4 ∈ Aᶜ, we can conclude both 4 ∈ U and 4 ∉ A. Option B contradicts the definition of a complement, option C contradicts membership in U, and option D is impossible because A ∩ Aᶜ = ∅.
Frequently asked questions
What is the correct answer to this question?
4 ∈ U and 4 ∉ A
Why is this the correct answer?
Membership in the complement Aᶜ means that the element is part of the universal set U but is excluded from A. Therefore, from 4 ∈ Aᶜ, we can conclude both 4 ∈ U and 4 ∉ A. Option B contradicts the definition of a complement, option C contradicts membership in U, and option D is impossible because A ∩ Aᶜ = ∅.
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.
