If n(U) = 60 and n(A ∪ B) = 45, how many elements are in (A ∪ B)'?
Answer and explanation
Correct answer: 15
The complement of A ∪ B consists of all elements in the universal set U that are not in the union. For a finite universal set, n((A ∪ B)') = n(U) − n(A ∪ B). Substituting the values gives 60 − 45 = 15. Thus, option A is correct. In a Venn diagram, this is the area of the rectangle outside both circles.
Frequently asked questions
What is the correct answer to this question?
15
Why is this the correct answer?
The complement of A ∪ B consists of all elements in the universal set U that are not in the union. For a finite universal set, n((A ∪ B)') = n(U) − n(A ∪ B). Substituting the values gives 60 − 45 = 15. Thus, option A is correct. In a Venn diagram, this is the area of the rectangle outside both circles.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: The Empty Set, many more. Step 3: Hence the set is infinite..
