P: True.
Q: If every edge weight is increased by the same value, the shortest path between any pair of vertices does not change. This statement will be true for trees as there will be a unique path between any pair of vertices in a tree. But here in this question, we are asked for any graph in general so there are possibilities of multiple paths.
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Suppose in a graph with 3 vertices a,b,c vertices are connected like this a-b-c and also a is directly connected to c. Edge weights are (a,b,2),(b,c,3),(a,c,6). Here shortest path between (a,c) is a to c via b. Now each edge weight is increased by the same value(suppose some value > 2). Now you will find a-c direct path as the shortest one, so our shortest path changed.
So Q False.