In a Venn diagram, the shaded region is outside both A and B. Which representation is correct?
Answer and explanation
Correct answer: A′ ∩ B′
The region outside A is A′, and the region outside B is B′. To be outside both sets simultaneously, an element must belong to A′ ∩ B′. By De Morgan’s law, this is also equal to (A ∪ B)′. In contrast, A ∪ B includes elements in at least one set, A ∩ B is the overlap, and A − B lies inside A. Therefore option A is correct.
Frequently asked questions
What is the correct answer to this question?
A′ ∩ B′
Why is this the correct answer?
The region outside A is A′, and the region outside B is B′. To be outside both sets simultaneously, an element must belong to A′ ∩ B′. By De Morgan’s law, this is also equal to (A ∪ B)′. In contrast, A ∪ B includes elements in at least one set, A ∩ B is the overlap, and A − B lies inside A. Therefore option A is correct.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
