Question

​Given that set A has 31 elements, set B has 8 elements, and set C has...

​Given that set A has 31 elements, set B has 8 elements, and set C has 11 elements, determine the maximum possible number of elements in A U B U C and the minimum possible number of elements in A U B U C

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Answer #1

The event A U B U C will have maximum number of elements when all the sets A, B and C are disjoint (have no elements in common).

Maximum possible number of elements in A U B U C = 31 + 8 + 11

= 50

The event A U B U C will have least number of elements when the two smaller subsets are subsets of the largest set. Here, the largest set is A with 31 elements. When B and C are subsets of A U B U C will have least number of events.

Minimum possible number of elements in A U B U C = 31

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