Answer to Question #336930 in Discrete Mathematics for Ashir

Question

Three sets have 5, 10, and 15 elements, respectively. How many elements can their union and their intersection have?

Answer 1

The union is the set combining all the elements from all three sets.

So, there could not be more elements then the sum of 5, 10 and 15 (when sets are disjoint, the union has exactly 30 elements). And not less then in the largest set (when the largest set consists other sets, then the union has 15 elements)

The intersection is the set of all distinct elements that are in all three sets.

So, there could not be more elements than in the smallest set (when the smallest set is contained in other, then the intersection has 5 elements). And when sets are disjoint, then their intersection is empty set. So, there are 0 elements.

Answer: the union can have from 15 to 30 elements; the intersection can have from 0 to 5 elements.