What region does \((A\cap B)^c\) represent in a Venn diagram?
Answer and explanation
Correct answer: All of U except \(A\cap B\)
The expression \((A\cap B)^c\) is the complement of the intersection. First, \(A\cap B\) is the overlapping region common to A and B. Taking its complement means selecting every point in the universal set U outside that overlap. Thus the answer includes the A-only region, the B-only region, and the region outside both sets, but excludes only the common overlap.
Frequently asked questions
What is the correct answer to this question?
All of U except \(A\cap B\)
Why is this the correct answer?
The expression \((A\cap B)^c\) is the complement of the intersection. First, \(A\cap B\) is the overlapping region common to A and B. Taking its complement means selecting every point in the universal set U outside that overlap. Thus the answer includes the A-only region, the B-only region, and the region outside both sets, but excludes only the common overlap.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
