If \(U\) is the set of all students in a school and \(A\) is the set of students who come by bus, what does \(A^c\) represent?
Answer and explanation
Correct answer: Students who do not come by bus
The complement \(A^c\) is defined relative to the universal set \(U\). It contains every student in the school who is not a member of \(A\), where membership in \(A\) means coming by bus. Therefore, \(A^c\) represents students who use another mode of travel or otherwise do not come by bus. It does not mean that there are no students.
Frequently asked questions
What is the correct answer to this question?
Students who do not come by bus
Why is this the correct answer?
The complement \(A^c\) is defined relative to the universal set \(U\). It contains every student in the school who is not a member of \(A\), where membership in \(A\) means coming by bus. Therefore, \(A^c\) represents students who use another mode of travel or otherwise do not come by bus. It does not mean that there are no students.
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.
