If n(A)=78, n(B)=69, n(C)=63, n(A∩B)=30, n(B∩C)=25, n(C∩A)=21, and n(A∩B∩C)=9, how many elements are only in set A?
Answer and explanation
Correct answer: 36
To obtain the region belonging only to A, subtract from n(A) the elements shared with B and the elements shared with C, then add the triple intersection once because it was subtracted twice. Thus, only A = n(A)−n(A∩B)−n(A∩C)+n(A∩B∩C) = 78−30−21+9 = 36. The B∩C value is not needed for this particular region. Therefore, option A is correct.
Frequently asked questions
What is the correct answer to this question?
36
Why is this the correct answer?
To obtain the region belonging only to A, subtract from n(A) the elements shared with B and the elements shared with C, then add the triple intersection once because it was subtracted twice. Thus, only A = n(A)−n(A∩B)−n(A∩C)+n(A∩B∩C) = 78−30−21+9 = 36. The B∩C value is not needed for this particular region. Therefore, option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
