If n(A)=11, n(B)=9, and n(A∩B)=4, what is the total number of elements in only A and only B?
Answer and explanation
Correct answer: 12
The elements only in A are those in A but not in B, so their number is n(A)−n(A∩B)=11−4=7. Similarly, the elements only in B number n(B)−n(A∩B)=9−4=5. Therefore, the requested total is 7+5=12, so option B is correct. Notice that 16 is n(A∪B), which includes the common four elements and therefore does not answer the question about exclusive regions.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The elements only in A are those in A but not in B, so their number is n(A)−n(A∩B)=11−4=7. Similarly, the elements only in B number n(B)−n(A∩B)=9−4=5. Therefore, the requested total is 7+5=12, so option B is correct. Notice that 16 is n(A∪B), which includes the common four elements and therefore does not answer the question about exclusive regions.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
