Dijkstra’s algorithms

Question

Consider a weighted, directed acyclic graph G = (V,E,w) in which edges that leave the source vertex s may have negative weights and all other edge weights are nonnegative. Does Dijkstra’s algorithm correctly compute the shortest-path weight δ(s,t) from s to every vertex t in this graph? Justify your answer

Answer 1

In case of -ve weight edges, dijkstra's may or may not failed, depending on the source vertex and Graph structure.

Answer 2

Dijkstra's algorithm can be applied on directed graphs that are having - ve edges , but in case if there is a negative cycle then dijkstra algorithm fails to provide correct solution.

in this question it is given a Directed Acyclic Graph which has a property that from any vertex if we take an outgoing edge then there will be no way to come back to that vertex again , that means there will be no cycle not even a positive weight cycle and no -ve weight cycle so in my opinion we can apply Dijkstras algorithm.