If n(A ∩ Bᶜ) = 33, n(Aᶜ ∩ B) = 27, n(A ∩ B) = 18, and n(U) = 110, what is n(Aᶜ ∩ Bᶜ)?
Answer and explanation
Correct answer: 32
The sets A and B divide U into four mutually disjoint regions: \(A\cap B^c\), \(A^c\cap B\), \(A\cap B\), and \(A^c\cap B^c\). Their cardinalities add to \(n(U)\). Therefore the missing region has size \(110-(33+27+18)=110-78=32\). Hence option A is correct; 78 is the sum of the three given regions, not the missing one.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
The sets A and B divide U into four mutually disjoint regions: \(A\cap B^c\), \(A^c\cap B\), \(A\cap B\), and \(A^c\cap B^c\). Their cardinalities add to \(n(U)\). Therefore the missing region has size \(110-(33+27+18)=110-78=32\). Hence option A is correct; 78 is the sum of the three given regions, not the missing one.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
