1. The following questions highlight the dierences between MSA and its undirected counterpart MST.

(a) Give an example of a digraph in which the lightest edge does not belong to any MSA rooted at r, even though it does belong to some SA rooted at r.

(b) Give an example of a digraph in which the heaviest edge belongs to each MSA rooted at r, even though there are some SA rooted at r that avoids it.

(c) Give an example of a digraph in which all edge weights are distinct but the MSA is not unique.

Please draw digraph and explain clearly in each step.