In a Venn diagram, which region represents \(A^c\) with respect to the universal set \(U\)?
Answer and explanation
Correct answer: The region inside \(U\) but outside \(A\)
By definition, the complement \(A^c\) consists of every element in the universal set \(U\) that does not belong to \(A\). In a Venn diagram, \(U\) is normally shown as a rectangle and \(A\) as a circle inside it. Therefore, \(A^c\) is the portion of the rectangle outside the circle, not the area outside the rectangle.
Frequently asked questions
What is the correct answer to this question?
The region inside \(U\) but outside \(A\)
Why is this the correct answer?
By definition, the complement \(A^c\) consists of every element in the universal set \(U\) that does not belong to \(A\). In a Venn diagram, \(U\) is normally shown as a rectangle and \(A\) as a circle inside it. Therefore, \(A^c\) is the portion of the rectangle outside the circle, not the area outside the rectangle.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
