Maximum flow properties
A helpful way to build intuition: Try working through an example!  Can you find an example of a graph and a flow where property (a) is true?  Then, ask yourself: is property (b) true in that one?  What made the difference?

Spoiler (but it's best to try the above first; it will help you learn more from this exercise):


   The crucial difference is between "for every maximum flow" vs "there exists a maximum flow".  That's the difference between $\forall$ vs $\exists$.  As you probably know, $\forall x . P(x)$ can be false even if $\exists x . P(x)$ is true.