If the universal set \(U=\{1,2,3,4,5,6,7,8,9\}\) and \(A=\{2,4,6\}\), what is the value of \(A^c\setminus\{1,3,5\}\)?
Answer and explanation
Correct answer: \(\{7,8,9\}\)
The complement of \(A\) is formed by taking all elements of the universal set that are not in \(A\). Therefore, \(A^c=U\setminus A=\{1,3,5,7,8,9\}\). The expression then asks us to remove \(\{1,3,5\}\) from this complement. The elements left are \(\{7,8,9\}\), so option A is correct. Option B stops after finding the complement and does not perform the set difference.
Frequently asked questions
What is the correct answer to this question?
\(\{7,8,9\}\)
Why is this the correct answer?
The complement of \(A\) is formed by taking all elements of the universal set that are not in \(A\). Therefore, \(A^c=U\setminus A=\{1,3,5,7,8,9\}\). The expression then asks us to remove \(\{1,3,5\}\) from this complement. The elements left are \(\{7,8,9\}\), so option A is correct. Option B stops after finding the complement and does not perform the set difference.
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.
