If the universal set is \(U=\{1,2,\ldots,24\}\), \(A=\{x:x\in U\text{ and }x\text{ is even}\}\), and \(B=\{x:x\in U\text{ and }x\text{ is odd}\}\), what is the relation between \(A'\) and \(B\)?
Answer and explanation
Correct answer: \(A'=B\)
Within the universal set \(U=\{1,2,\ldots,24\}\), set \(A\) contains exactly the even numbers. Its complement therefore contains every element of \(U\) that is not even, namely the odd numbers \(\{1,3,5,\ldots,23\}\). Set \(B\) is defined as precisely this collection of odd numbers. Consequently, \(A'=B\). Option B is false because the two sets are equal, not a proper subset.
Frequently asked questions
What is the correct answer to this question?
\(A'=B\)
Why is this the correct answer?
Within the universal set \(U=\{1,2,\ldots,24\}\), set \(A\) contains exactly the even numbers. Its complement therefore contains every element of \(U\) that is not even, namely the odd numbers \(\{1,3,5,\ldots,23\}\). Set \(B\) is defined as precisely this collection of odd numbers. Consequently, \(A'=B\). Option B is false because the two sets are equal, not a proper subset.
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.
