4. (Total order, 12pt) Below we show a relation between nine tasks (labeled 1 to 9), created using https //graphon11neru/en/ you can download the graph as th. 4. hrnl from the week 5 folder). A directed arrow, e g. from 2 to 6 means that 2 needs to come before 6. This relation determines a partial order if we add the missing transitive relations (e. g. we have 9 comes before 2 and 2 comes before 6 so in a mt we'd need to have 9 comes before 6; this is not explicitly drawn in the diagram, since there'd be too many arrows). a) [2pt] Does the pgset described by the graph contain a minimum (not minimal) element? If so state the minimum element, and, either way, argue why it is minimum, or why there is no minimum element. Hint: how do you recognize a minimum element m the graph? b) [2pt] Does the pose; described by the Q3 graph contain a maximum (not maximal) element? If so state the maximum element, and, either way, argue why it is maximum, or why there is no maximum element. Hint: see hint for part a). c) [6pt] Create a total order consistent with the given relation using the algorithm we saw in class: nd a minimal element, make it rst, remove it, and continue For each of the nine steps show: the minimal element you pick _and_ what the remaining graph looks like, (You can use https: //graphonline. ru/en/) to redraw the graph. d) [2pt] Explicitly state a total order consistent with the relation given in the diagram