If n(A) = 90, n(B) = 85, n(A ∪ B) = 125, and n(U) = 160, what is n(Aᶜ ∩ Bᶜ)?
Answer and explanation
Correct answer: 35
De Morgan’s law states that \(A^c\cap B^c=(A\cup B)^c\). Thus the required set contains precisely the elements of \(U\) that are outside the union. Its cardinality is \(n(U)-n(A\cup B)=160-125=35\). Therefore option A is correct. The separate values of \(n(A)\) and \(n(B)\) are not needed once the union is known.
Frequently asked questions
What is the correct answer to this question?
35
Why is this the correct answer?
De Morgan’s law states that \(A^c\cap B^c=(A\cup B)^c\). Thus the required set contains precisely the elements of \(U\) that are outside the union. Its cardinality is \(n(U)-n(A\cup B)=160-125=35\). Therefore option A is correct. The separate values of \(n(A)\) and \(n(B)\) are not needed once the union is known.
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.
