In a class, n(U) = 80, n(A) = 37, n(B) = 42, and n(A ∩ B) = 19. How many students belong only to A?
Answer and explanation
Correct answer: 18
The set A contains both the students who belong only to A and the students common to A and B. Thus n(A) = n(only A) + n(A ∩ B). Therefore, n(only A) = 37 − 19 = 18. The universal-set size and the total size of B are unnecessary for this particular question. Subtracting the common region once prevents those students from being counted as exclusive members of A.
Frequently asked questions
What is the correct answer to this question?
18
Why is this the correct answer?
The set A contains both the students who belong only to A and the students common to A and B. Thus n(A) = n(only A) + n(A ∩ B). Therefore, n(only A) = 37 − 19 = 18. The universal-set size and the total size of B are unnecessary for this particular question. Subtracting the common region once prevents those students from being counted as exclusive members of A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
