If n(U) = 100, n(A) = 48, n(B) = 46, and n((A union B) complement) = 18, what is n(A intersection B)?
Answer and explanation
Correct answer: 12
The complement of A union B contains the elements outside both A and B. Therefore, n(A union B) = n(U) − n((A union B) complement) = 100 − 18 = 82. For two finite sets, n(A union B) = n(A) + n(B) − n(A intersection B). Substituting gives 82 = 48 + 46 − n(A intersection B), so n(A intersection B) = 94 − 82 = 12. Thus option B is correct.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The complement of A union B contains the elements outside both A and B. Therefore, n(A union B) = n(U) − n((A union B) complement) = 100 − 18 = 82. For two finite sets, n(A union B) = n(A) + n(B) − n(A intersection B). Substituting gives 82 = 48 + 46 − n(A intersection B), so n(A intersection B) = 94 − 82 = 12. Thus option B is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
