Consider a network with capacities c(e) over edges. Say that we found the maximum flow function from s to t. Denote by f(e) the flow on e. Say that we choose one of the directed edges e and increase the capacity of this edge e by 1. Namely the capacity of e is c(e) + 1 now. The following question can be true or false. Hence answer for each one of them if its true or false and prove your answer. Saying only yes/no will not get many points.

2. It may be that the flow value increased by 2 after the change.