Show that if a network $\displaystyle N$ contains no directed path from the source $\displaystyle s$ to the sink $\displaystyle t$, then the maximum possible total flow on $\displaystyle N$ (for any flow function) is $\displaystyle 0$.


I am not sure how to prove this. I know I want to use the max flow min cut theorem that would show that the value of a maximum flow and the capacity of a minimum cut are both zero. So, I need some help with this one. Thanks in advance.