If P ∩ Q = ∅ and P ∪ Q = U, then Pᶜ is equal to which set?
Answer and explanation
Correct answer: Q
The condition P ∩ Q = ∅ says that P and Q have no common elements, while P ∪ Q = U says that together they contain every element of the universal set. Thus, every element not in P must be in Q, and every element of Q is outside P. Therefore, Q is exactly the complement of P in U: Pᶜ = Q. Hence, option A is correct.
Frequently asked questions
What is the correct answer to this question?
Q
Why is this the correct answer?
The condition P ∩ Q = ∅ says that P and Q have no common elements, while P ∪ Q = U says that together they contain every element of the universal set. Thus, every element not in P must be in Q, and every element of Q is outside P. Therefore, Q is exactly the complement of P in U: Pᶜ = Q. Hence, option A is correct.
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.
