If the universal set is \(U=\{1,2,3,4,5,6,7,8,9\}\), \(A=\{1,2,3,4\}\), and \(B=\{4,5,6\}\), what is the value of \(A^c-B^c\)?
Advertisement
Answer and explanation
Correct answer: \(\{5,6\}\)
With respect to \(U\), \(A^c=\{5,6,7,8,9\}\) and \(B^c=\{1,2,3,7,8,9\}\). The difference \(A^c-B^c\) retains elements in \(A^c\) that are not in \(B^c\), giving \(\{5,6\}\). Equivalently, \(X-Y=X\cap Y^c\), so \(A^c-B^c=A^c\cap B\). Thus option A is correct.
Frequently asked questions
What is the correct answer to this question?
\(\{5,6\}\)
Why is this the correct answer?
With respect to \(U\), \(A^c=\{5,6,7,8,9\}\) and \(B^c=\{1,2,3,7,8,9\}\). The difference \(A^c-B^c\) retains elements in \(A^c\) that are not in \(B^c\), giving \(\{5,6\}\). Equivalently, \(X-Y=X\cap Y^c\), so \(A^c-B^c=A^c\cap B\). Thus 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