If A is a set with 63 elements and B is a set with 45 elements, what is the minimum number of elements in A ∪ B?

Question

How would I figure this out? 

Answer 1

The minimum value for the union of A and B would occur when B is a proper subset of A; that is, all 45 elements in set B are already in set A.  So:

 

n(A U B) = 63

 

That would be the minimum value for A U B.

Answer 2

The smallest possible union is if B is a subset of A. 

So 63