If \(A-B=\{p,q\}\), \(A\cap B=\{r,s,t\}\), and \(B-A=\{u\}\), what is the value of \(n(A)\)?
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Answer and explanation
Correct answer: 5
The elements of set \(A\) are divided into two disjoint parts: those belonging only to \(A\), represented by \(A-B\), and those common to both sets, represented by \(A\cap B\). Their sizes are 2 and 3 respectively. Thus \(n(A)=2+3=5\). The element in \(B-A\) belongs only to \(B\), so it is not counted.
Frequently asked questions
What is the correct answer to this question?
5
Why is this the correct answer?
The elements of set \(A\) are divided into two disjoint parts: those belonging only to \(A\), represented by \(A-B\), and those common to both sets, represented by \(A\cap B\). Their sizes are 2 and 3 respectively. Thus \(n(A)=2+3=5\). The element in \(B-A\) belongs only to \(B\), so it is not counted.
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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