If \(n(A)=20\), \(n(B)=25\), and \(A\cap B=\varnothing\), how many elements belong to exactly one set?
Answer and explanation
Correct answer: 45
Because A and B are disjoint, no element is counted in both sets. Consequently, every element of A belongs to exactly one set, and every element of B also belongs to exactly one set. The required count is therefore \(n(A)+n(B)=20+25=45\). If the sets overlapped, their common elements would have to be subtracted from this sum.
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What is the correct answer to this question?
45
Why is this the correct answer?
Because A and B are disjoint, no element is counted in both sets. Consequently, every element of A belongs to exactly one set, and every element of B also belongs to exactly one set. The required count is therefore \(n(A)+n(B)=20+25=45\). If the sets overlapped, their common elements would have to be subtracted from this sum.
Which subject and chapter does this question cover?
This is a Class 12 Mathematics question. Chapter: Sets.
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