If n(U) = 58 and n(A ∪ B) = 41, how many elements are in the region neither in A nor in B?
Answer and explanation
Correct answer: 17
Elements that are neither in A nor in B lie outside the union A ∪ B, so they form the complement (A ∪ B)′ within the universal set U. The universal set is partitioned into the union and its complement. Therefore n((A ∪ B)′) = n(U) − n(A ∪ B) = 58 − 41 = 17. Option A is correct; 41 is the union itself and 58 is the total universe.
Frequently asked questions
What is the correct answer to this question?
17
Why is this the correct answer?
Elements that are neither in A nor in B lie outside the union A ∪ B, so they form the complement (A ∪ B)′ within the universal set U. The universal set is partitioned into the union and its complement. Therefore n((A ∪ B)′) = n(U) − n(A ∪ B) = 58 − 41 = 17. Option A is correct; 41 is the union itself and 58 is the total universe.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
