If the universal set is \(U=\{1,2,\ldots,12\}\), \(A=\{2,4,6,8,10,12\}\), and \(B=\{3,6,9,12\}\), what is the complement of \(A-B\) with respect to \(U\)?
Answer and explanation
Correct answer: \(\{1,3,5,6,7,9,11,12\}\)
The difference \(A-B\) contains the elements of \(A\) that are not in \(B\). Since 6 and 12 occur in both sets, \(A-B=\{2,4,8,10\}\). The complement is taken relative to the stated universal set \(U\), so remove these four elements from \(\{1,2,\ldots,12\}\). Therefore, \((A-B)'=\{1,3,5,6,7,9,11,12\}\), which is option A. Option B is the difference itself, not its complement.
Frequently asked questions
What is the correct answer to this question?
\(\{1,3,5,6,7,9,11,12\}\)
Why is this the correct answer?
The difference \(A-B\) contains the elements of \(A\) that are not in \(B\). Since 6 and 12 occur in both sets, \(A-B=\{2,4,8,10\}\). The complement is taken relative to the stated universal set \(U\), so remove these four elements from \(\{1,2,\ldots,12\}\). Therefore, \((A-B)'=\{1,3,5,6,7,9,11,12\}\), which is option A. Option B is the difference itself, not its complement.
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.
