If \(n(U)=75\) and \(n(A\cap B)=18\), what is \(n((A\cap B)^c)\)?
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Answer and explanation
Correct answer: 57
For any finite set X contained in the universal set U, the number of elements in its complement is \(n(X^c)=n(U)-n(X)\). Here, take \(X=A\cap B\). Therefore, \(n((A\cap B)^c)=75-18=57\). The value 18 is the intersection itself, while 75 is the entire universal set. Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
57
Why is this the correct answer?
For any finite set X contained in the universal set U, the number of elements in its complement is \(n(X^c)=n(U)-n(X)\). Here, take \(X=A\cap B\). Therefore, \(n((A\cap B)^c)=75-18=57\). The value 18 is the intersection itself, while 75 is the entire universal set. Hence option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
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