If \(U=\{1,2,3,4,5,6,7,8,9,10,11,12\}\) and \(A=\{3,6,9,12\}\), how many elements does \(A'\) contain?
Advertisement
Answer and explanation
Correct answer: 8
The universal set has 12 elements, so \(n(U)=12\). The set \(A=\{3,6,9,12\}\) has 4 elements, so \(n(A)=4\). For a finite universal set, a set and its complement partition the universal set; therefore, \(n(A')=n(U)-n(A)=12-4=8\). Hence option A is correct.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
The universal set has 12 elements, so \(n(U)=12\). The set \(A=\{3,6,9,12\}\) has 4 elements, so \(n(A)=4\). For a finite universal set, a set and its complement partition the universal set; therefore, \(n(A')=n(U)-n(A)=12-4=8\). Hence 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.
Advertisement