If we have two sets, A and B, contained in the universal set
Can someone tell me why the smallest possible number of elements of
(A intersect B) occurs when A union B = universal set???
i know that
n(A intersect B) = n(A) + n(B) - n(A union B)
so to make it smaller, we need to make n(A union B) as big as possible.
But is there a way to explain this without using the formula above???
A and B. The smallest number that could be shared is 6 (that is:
n(A)+n(B)-n(U), any smaller number of shared elements will leave n(A Union
B)>60, which would be a contradiction).
But if A and B share exactly 6 elements then n(A Union B)=60, and so
A Union B=U.