If only A has 12 elements, A∩B has 5 elements, and only B has 8 elements, what is n(A∪B)?
Advertisement
Answer and explanation
Correct answer: 25
The union A∪B contains every element that lies in A, in B, or in their intersection. The three stated Venn-diagram regions are disjoint, so each must be counted exactly once: n(A∪B)=12+5+8=25. Therefore option C is correct. Adding only the exclusive regions would give 20 and would wrongly omit the five common elements.
Frequently asked questions
What is the correct answer to this question?
25
Why is this the correct answer?
The union A∪B contains every element that lies in A, in B, or in their intersection. The three stated Venn-diagram regions are disjoint, so each must be counted exactly once: n(A∪B)=12+5+8=25. Therefore option C is correct. Adding only the exclusive regions would give 20 and would wrongly omit the five common elements.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
Advertisement