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???