If the universal set is \(U=\{x\in\mathbb{Z}:-5\le x\le 5\}\) and \(A=\{x\in U:x^2=9\}\), how many elements does the complement \(A^c\) contain?
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Answer and explanation
Correct answer: 9
The integers from -5 through 5 give 11 elements in U. Solving \(x^2=9\) gives \(x=3\) or \(x=-3\), both of which belong to U; therefore \(A=\{-3,3\}\) and \(n(A)=2\). The complement has the remaining elements, so \(n(A^c)=n(U)-n(A)=11-2=9\). Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
The integers from -5 through 5 give 11 elements in U. Solving \(x^2=9\) gives \(x=3\) or \(x=-3\), both of which belong to U; therefore \(A=\{-3,3\}\) and \(n(A)=2\). The complement has the remaining elements, so \(n(A^c)=n(U)-n(A)=11-2=9\). Thus option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Complement of a Set and Its Properties.
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