If \(n(B-A)=8\) and \(n(A\cap B)=4\), what is \(n(B)\)?
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Answer and explanation
Correct answer: 12
The set \(B\) consists of two non-overlapping parts: the elements only in \(B\), represented by \(B-A\), and the elements common to both sets, represented by \(A\cap B\). Thus, \(n(B)=n(B-A)+n(A\cap B)=8+4=12\). Therefore, option C is correct. Neither 8 nor 4 represents the entire set \(B\), and 32 is an unjustified product.
Frequently asked questions
What is the correct answer to this question?
12
Why is this the correct answer?
The set \(B\) consists of two non-overlapping parts: the elements only in \(B\), represented by \(B-A\), and the elements common to both sets, represented by \(A\cap B\). Thus, \(n(B)=n(B-A)+n(A\cap B)=8+4=12\). Therefore, option C is correct. Neither 8 nor 4 represents the entire set \(B\), and 32 is an unjustified product.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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