If n(A − B) = 36, n(B − A) = 28, n(A ∩ B) = 22, and n(U) = 120, what is n(Aᶜ ∪ Bᶜ)?
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Answer and explanation
Correct answer: 98
De Morgan’s law gives \(A^c\cup B^c=(A\cap B)^c\). Thus every element of the universal set is included except the 22 elements in \(A\cap B\). Consequently, \(n(A^c\cup B^c)=n(U)-n(A\cap B)=120-22=98\). Option D is correct. The other regional counts are consistent but unnecessary for this particular identity.
Frequently asked questions
What is the correct answer to this question?
98
Why is this the correct answer?
De Morgan’s law gives \(A^c\cup B^c=(A\cap B)^c\). Thus every element of the universal set is included except the 22 elements in \(A\cap B\). Consequently, \(n(A^c\cup B^c)=n(U)-n(A\cap B)=120-22=98\). Option D is correct. The other regional counts are consistent but unnecessary for this particular identity.
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.
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