If \(U=\{1,2,\ldots,10\}\) and \(A=\{x\in U:x\text{ is a multiple of 2 or 3}\}\), what is \(A'\)?
Answer and explanation
Correct answer: \(\{1,5,7\}\)
Within the universal set \(U\), the multiples of 2 are \(\{2,4,6,8,10\}\), and the multiples of 3 are \(\{3,6,9\}\). Taking their union gives \(A=\{2,3,4,6,8,9,10\}\). The complement \(A'\) contains precisely those elements of \(U\) that are not in \(A\). Removing these seven elements from \(U\) leaves \(A'=\{1,5,7\}\). Thus option A is correct; option B is the set \(A\) itself.
Frequently asked questions
What is the correct answer to this question?
\(\{1,5,7\}\)
Why is this the correct answer?
Within the universal set \(U\), the multiples of 2 are \(\{2,4,6,8,10\}\), and the multiples of 3 are \(\{3,6,9\}\). Taking their union gives \(A=\{2,3,4,6,8,9,10\}\). The complement \(A'\) contains precisely those elements of \(U\) that are not in \(A\). Removing these seven elements from \(U\) leaves \(A'=\{1,5,7\}\). Thus option A is correct; option B is the set \(A\) itself.
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.
