If \(A\cap B=\varnothing\), which formula for \(|A\cup B|\) is correct?
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Answer and explanation
Correct answer: \(|A|+|B|\)
For any two finite sets, \(|A\cup B|=|A|+|B|-|A\cap B|\). Here \(A\cap B=\varnothing\), so the intersection has cardinality zero. Substitution gives \(|A\cup B|=|A|+|B|-0=|A|+|B|\). The sets are disjoint, so no element is counted twice. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(|A|+|B|\)
Why is this the correct answer?
For any two finite sets, \(|A\cup B|=|A|+|B|-|A\cap B|\). Here \(A\cap B=\varnothing\), so the intersection has cardinality zero. Substitution gives \(|A\cup B|=|A|+|B|-0=|A|+|B|\). The sets are disjoint, so no element is counted twice. Hence option A is correct.
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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