If n(A − B) = 10 and n(A ∩ B) = 7, what is n(A)?
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Answer and explanation
Correct answer: 17
The set A is divided into two non-overlapping parts: elements only in A, represented by A − B, and elements common to A and B, represented by A ∩ B. Therefore n(A) = n(A − B) + n(A ∩ B) = 10 + 7 = 17. Option B counts only the exclusive part and ignores the common elements, so it is incomplete.
Frequently asked questions
What is the correct answer to this question?
17
Why is this the correct answer?
The set A is divided into two non-overlapping parts: elements only in A, represented by A − B, and elements common to A and B, represented by A ∩ B. Therefore n(A) = n(A − B) + n(A ∩ B) = 10 + 7 = 17. Option B counts only the exclusive part and ignores the common elements, so it is incomplete.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Operations on Sets (Union, Intersection, Difference).
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