If 5 ∉ Aᶜ and 5 ∈ U, which statement is correct?
Answer and explanation
Correct answer: 5 ∈ A
For an element of the universal set U, membership is divided between A and its complement Aᶜ: every element of U is in exactly one of these two sets. Since 5 belongs to U but is explicitly not in Aᶜ, it must belong to A. Option C contradicts the given condition, option B contradicts 5 ∈ U, and option D is impossible because A ∩ Aᶜ is empty.
Frequently asked questions
What is the correct answer to this question?
5 ∈ A
Why is this the correct answer?
For an element of the universal set U, membership is divided between A and its complement Aᶜ: every element of U is in exactly one of these two sets. Since 5 belongs to U but is explicitly not in Aᶜ, it must belong to A. Option C contradicts the given condition, option B contradicts 5 ∈ U, and option D is impossible because A ∩ Aᶜ is empty.
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.
