If n(U)=90 and n(A ∪ B ∪ C)=76, how many elements are in none of the sets?
Answer and explanation
Correct answer: 14
The union A ∪ B ∪ C contains every element belonging to at least one of the three sets. Therefore, elements in none of the sets are in its complement within U. Using the complement-count rule, the number is n(U) − n(A ∪ B ∪ C) = 90 − 76 = 14. Hence option A is correct. The value 76 counts elements in at least one set, while 90 is the total universal-set size.
Frequently asked questions
What is the correct answer to this question?
14
Why is this the correct answer?
The union A ∪ B ∪ C contains every element belonging to at least one of the three sets. Therefore, elements in none of the sets are in its complement within U. Using the complement-count rule, the number is n(U) − n(A ∪ B ∪ C) = 90 − 76 = 14. Hence option A is correct. The value 76 counts elements in at least one set, while 90 is the total universal-set size.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
