Answer to Question #336431 in Discrete Mathematics for Ashir

Question

We form the union of a set with 5 elements and a set with 9 elements. Which of the following numbers can we get as the cardinality of the union: 4, 6, 9, 10, 14, 20?

Answer 1

So, the smallest [A∪B] is when all elements of A are also elements of B. Then, [A∪B] in this case is:(those 5 similar elements) + (the remaining 4 in B) = 9

And the largest [A∪B] is when no element of A is in B Then, [A∪B] in this case is:[A] + [B] = 14

Then the possible cardinalities of [A∪B] are

9, 10, ... , 14