If \(U=\{0,1,2,3,4,5,6\}\) and \(A=\{1,3,5\}\), what is \(n(A')\)?
Answer and explanation
Correct answer: 4
The complement \(A'\) contains all elements of the universal set \(U\) that are not elements of \(A\). Removing 1, 3, and 5 from \(U\) gives \(A'=\{0,2,4,6\}\). This set has four elements, so \(n(A')=4\). The same result follows from the formula \(n(A')=n(U)-n(A)=7-3=4\). Thus option B is correct; 3 is the size of \(A\), while 7 is the size of \(U\).
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The complement \(A'\) contains all elements of the universal set \(U\) that are not elements of \(A\). Removing 1, 3, and 5 from \(U\) gives \(A'=\{0,2,4,6\}\). This set has four elements, so \(n(A')=4\). The same result follows from the formula \(n(A')=n(U)-n(A)=7-3=4\). Thus option B is correct; 3 is the size of \(A\), while 7 is the size of \(U\).
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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