In three sets, how do we find the number of elements in only A?
Answer and explanation
Correct answer: n(A) − n(A ∩ B) − n(A ∩ C) + n(A ∩ B ∩ C)
To obtain the region belonging only to A, begin with all elements of A. Remove the elements shared by A and B and those shared by A and C. The elements in A ∩ B ∩ C were removed twice in those two subtractions, so add them back once. Therefore, Only A = n(A)−n(A ∩ B)−n(A ∩ C)+n(A ∩ B ∩ C).
Frequently asked questions
What is the correct answer to this question?
n(A) − n(A ∩ B) − n(A ∩ C) + n(A ∩ B ∩ C)
Why is this the correct answer?
To obtain the region belonging only to A, begin with all elements of A. Remove the elements shared by A and B and those shared by A and C. The elements in A ∩ B ∩ C were removed twice in those two subtractions, so add them back once. Therefore, Only A = n(A)−n(A ∩ B)−n(A ∩ C)+n(A ∩ B ∩ C).
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
