Why do A, B, and C create 7 separate inner regions in a Venn diagram?
Answer and explanation
Correct answer: Because the non-empty membership types are 2^3 − 1 = 7
For each of the three sets, an element may be inside or outside that set. Thus there are 2 choices for each set and 2 × 2 × 2 = 2^3 = 8 membership patterns. One pattern means being outside A, outside B, and outside C simultaneously; it is the region outside all three circles. The remaining 8 − 1 = 7 patterns correspond to membership in at least one set, so they form the seven inner regions.
Frequently asked questions
What is the correct answer to this question?
Because the non-empty membership types are 2^3 − 1 = 7
Why is this the correct answer?
For each of the three sets, an element may be inside or outside that set. Thus there are 2 choices for each set and 2 × 2 × 2 = 2^3 = 8 membership patterns. One pattern means being outside A, outside B, and outside C simultaneously; it is the region outside all three circles. The remaining 8 − 1 = 7 patterns correspond to membership in at least one set, so they form the seven inner regions.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Sets. Topic: Venn Diagrams.
