If n(U) = 88, n(A − B) = 24, n(A ∩ B) = 13, and n(B − A) = 26, what is the number of elements in the outside region of the Venn diagram?
Advertisement
Answer and explanation
Correct answer: 25
The universal set is divided into four regions: A only, A ∩ B, B only, and outside both sets. The three regions inside the union contain 24 + 13 + 26 = 63 elements. Therefore, the outside region contains n(U) − n(A ∪ B) = 88 − 63 = 25 elements. Hence, option A is correct.
Frequently asked questions
What is the correct answer to this question?
25
Why is this the correct answer?
The universal set is divided into four regions: A only, A ∩ B, B only, and outside both sets. The three regions inside the union contain 24 + 13 + 26 = 63 elements. Therefore, the outside region contains n(U) − n(A ∪ B) = 88 − 63 = 25 elements. Hence, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
Advertisement