For the following questions, select the true statement$($s$).$ No ex$-$

planation is necessary for these questions.

$($a$)$ What is true about the residual graph in the Ford$-$Fulkerson algorithm?

$$ The sum of residual capacities over all edges in the residual graph is equal to the

sum of the capacities in the original graph.

$$ The number of edges in the residual graph is at least equal to the number of

directed edges in the flow network.

$$ The capacity of any edge in residual graph does not exceed the capacity of the

corresponding edge in the flow network, if it exists.

$$ The capacity of an edge in the residual graph depends on the direction, quantity,

and capacities of the pipes between the two vertices.