I need question two In this question, we'll see how some changes to the edge weight can affect the MST or SSSP of the graph.(V, E), suppose all edges have distinct weights. Let T be the set of edges in1.For a graph Gthe MST of G.(a)If we double each edge weight (i.e., set the new weight to be 1+ original edge weight),will T still be the MST of the new graph? If so, prove it. If not, provide a counterexample.2.=(b)If we increase all edge weights by 1 (i.e., set the new weight to be 1+ original edge weight),will T still be the MST of the new graph? If so, prove it. If not, provide a counterexample.For a graph G (V, E), suppose for any pair of vertices, the shortest paths is unique. Let P bethe list of edges on the shortest path from some vertex s to t.=(a)(b)If we double each edge weight (i.e., set the new weight to be 2× original edge weight), willP still be the SSSP from s to t on the new graph? If so, prove it. If not, provide a counterexample.If we increase all edge weights by 1 (i.e., set the new weight to be 2× original edgeweight), will P still be the SSSP from s to t on the new graph? If so, prove it. If not, provide acounterexample.

As you have asked i have solved the second question below There won't be any change in the path from s to t in both the cases as each edge weight is being increased with either equal amount or being doubled(where the order still remains the same) The below image is explaination with an example: In the first example we can see that if the edge weight will be doubled the lower will still be lower and the higher will become more higher so the order still remains same. since the sum of a particular path is lesser than the sum of another path so multiplying each path would still give the same result. In the second example as each weight is increased by 1 there is a possibility that P could still be the answer and could also not be.The second possibility is explained in the image below: