If A and B are finite sets, n(A \ B) = 12, n(B) = 20, and n(A ∩ B) = 8, what is n(A ∪ B)?
Answer and explanation
Correct answer: 32
The set A is divided into the disjoint parts A \ B and A ∩ B. However, the union can be viewed more simply as the disjoint union of A \ B with all of B: elements outside B but in A contribute 12, and every element of B contributes 20. Therefore n(A ∪ B) = n(A \ B) + n(B) = 12 + 20 = 32. The common elements are already included in n(B), so they are not counted twice.
Frequently asked questions
What is the correct answer to this question?
32
Why is this the correct answer?
The set A is divided into the disjoint parts A \ B and A ∩ B. However, the union can be viewed more simply as the disjoint union of A \ B with all of B: elements outside B but in A contribute 12, and every element of B contributes 20. Therefore n(A ∪ B) = n(A \ B) + n(B) = 12 + 20 = 32. The common elements are already included in n(B), so they are not counted twice.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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