x7.1.3 Let N:-N(X, Y) be a network with source set X and sink set Y. Construct a new network N:- N'(x, y) as follows. d Adjoin two new vertices r and y Join x to each source by an arc of infinite capacity. > Join each sink to y by an arc of infinite capacity. For any flow f in N, consider the function f' defined on the arc set of N" by: f (a) if a is an arc of N f-(v) if a = (v, y) a) Show that f' is a flow in N" with the same value as f b) Show, conversely, that the restriction of a flow in N to the arc set of N isa flow in N of the same value. x7.1.3 Let N:-N(X, Y) be a network with source set X and sink set Y. Construct a new network N:- N'(x, y) as follows. d Adjoin two new vertices r and y Join x to each source by an arc of infinite capacity. > Join each sink to y by an arc of infinite capacity. For any flow f in N, consider the function f' defined on the arc set of N" by: f (a) if a is an arc of N f-(v) if a = (v, y) a) Show that f' is a flow in N" with the same value as f b) Show, conversely, that the restriction of a flow in N to the arc set of N isa flow in N of the same value