If x ∈ U and x ∉ A, then x will be an element of which set?
Answer and explanation
Correct answer: Aᶜ
An element belongs to the complement Aᶜ precisely when it is in the universal set U but not in A. The conditions x ∈ U and x ∉ A state exactly this membership rule, so x ∈ Aᶜ. It cannot be concluded that x belongs to A, because the second condition says the opposite. The empty set has no elements, and A ∩ Aᶜ is always empty.
Frequently asked questions
What is the correct answer to this question?
Aᶜ
Why is this the correct answer?
An element belongs to the complement Aᶜ precisely when it is in the universal set U but not in A. The conditions x ∈ U and x ∉ A state exactly this membership rule, so x ∈ Aᶜ. It cannot be concluded that x belongs to A, because the second condition says the opposite. The empty set has no elements, and A ∩ Aᶜ is always 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.
