I know the formula for finding the total and I know why this is not enough info, but I guess I don't really understand how to prove this with an example.
There is a class of all boys. We know that there are a boys who like to
play chess, b who like to play soccer, c who like biking and d who like hiking. The
number of those who like to play both chess and soccer is x. There are y boys
who like chess and biking, z boys who like chess and hiking, u who like soccer
and biking, v boys who like soccer and hiking, and finally w boys who like biking
and hiking. We don’t know how many boys like, e.g.,chess, soccer and hiking, but
we know that everybody likes at least one of these activities. We would like to
know how many boys are in the class.
(a) Show by an example that this is not determined by what we know.
(b) Prove that we can at least conclude that the number of boys in the class
is at most a + b + c + d, and at least a + b + c + d - x - y- z - u - v- w.