If \(U=\{1,2,3,4,5,6,7,8,9,10\}\) and \(A=\{1,4,9\}\), how many elements does \(A'\) have?
Answer and explanation
Correct answer: 7
The complement \(A'\) contains all elements of the universal set \(U\) that are not present in \(A\). The universal set has 10 elements, while \(A\) has 3 elements: 1, 4, and 9. Therefore, \(n(A')=n(U)-n(A)=10-3=7\). In fact, \(A'=\{2,3,5,6,7,8,10\}\), which confirms that it contains seven elements. Hence, option C is correct.
Frequently asked questions
What is the correct answer to this question?
7
Why is this the correct answer?
The complement \(A'\) contains all elements of the universal set \(U\) that are not present in \(A\). The universal set has 10 elements, while \(A\) has 3 elements: 1, 4, and 9. Therefore, \(n(A')=n(U)-n(A)=10-3=7\). In fact, \(A'=\{2,3,5,6,7,8,10\}\), which confirms that it contains seven elements. Hence, option C 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.
