$($a$)$ Dijkstra's algorithm assumes that there are no negative weights $($and thus no negative weight cycles$)$ in the graph. However, if we assume a graph has negative weights but no negative weight cycles, one possible modification for Dijkstra's algorithm is simply adjusting all the weights to make them positive using the following procedure:

Adjust the weights of all edges by a constant $($dependent on the value of the most negative weight$)$ such that all edge weights are positive

Run Dijkstra's algorithm to find shortest paths $($which must exist since there are no negative weight cycles$)$

Subtract the constant from the edges in the final paths

Provide a simple counterexample to show this modification could produce incorrect results.