Graduate Management Admission Test (GMAT) Practice Test

What can be determined from the total number of items in a Venn diagram involving three sets A, B, and C?

1. Only the intersection of all sets

2. The average of all sets

3. The individual counts of each set only

4. The combined total using inclusion-exclusion principle

The correct answer is: The combined total using inclusion-exclusion principle

The total number of items in a Venn diagram involving three sets A, B, and C can be effectively determined using the inclusion-exclusion principle. This principle allows us to account for overlaps between the sets, providing a comprehensive count that avoids double-counting elements that may belong to more than one set. When applying the inclusion-exclusion principle, you first count the number of items in each individual set. Then, you subtract the counts of the intersections of pairs of sets to correct for those items being counted multiple times. Finally, you add back in the count of the intersection of all three sets, as those elements were subtracted out too many times in the previous steps. This approach leads to an accurate total that reflects all elements across the three sets, making it clear why it is the correct answer. It goes beyond merely identifying intersections or obtaining averages, as it deals with the complete picture of how many distinct items are represented when considering all three sets together.