If n(A−B)=44, n(B−A)=36, n(A∩B)=29, and n(U)=150, what is n(Aᶜ∪Bᶜ)?
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Answer and explanation
Correct answer: 121
De Morgan’s law gives Aᶜ∪Bᶜ=(A∩B)ᶜ. Thus, the requested set consists of every universal-set element except those in the intersection A∩B. Since U has 150 elements and A∩B has 29 elements, n(Aᶜ∪Bᶜ)=150−29=121. The difference-region values are consistent with the diagram but are not needed for this calculation.
Frequently asked questions
What is the correct answer to this question?
121
Why is this the correct answer?
De Morgan’s law gives Aᶜ∪Bᶜ=(A∩B)ᶜ. Thus, the requested set consists of every universal-set element except those in the intersection A∩B. Since U has 150 elements and A∩B has 29 elements, n(Aᶜ∪Bᶜ)=150−29=121. The difference-region values are consistent with the diagram but are not needed for this calculation.
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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