If n(A)=102, n(B)=95, n(A∪B)=143, and n(U)=190, what is n(Aᶜ∩Bᶜ)?
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Answer and explanation
Correct answer: 47
De Morgan’s law states that Aᶜ∩Bᶜ=(A∪B)ᶜ. Thus, Aᶜ∩Bᶜ represents the elements in the universal set that lie outside A∪B. Since the universal set has 190 elements and the union contains 143 elements, the required number is 190−143=47. The individual values n(A) and n(B) are not needed after the union is given.
Frequently asked questions
What is the correct answer to this question?
47
Why is this the correct answer?
De Morgan’s law states that Aᶜ∩Bᶜ=(A∪B)ᶜ. Thus, Aᶜ∩Bᶜ represents the elements in the universal set that lie outside A∪B. Since the universal set has 190 elements and the union contains 143 elements, the required number is 190−143=47. The individual values n(A) and n(B) are not needed after the union is given.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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