Let $$G$$ be a weighted connected undirected graph with distinct positive edge weights. If every edge weight is increased by the same value, then which of the following statements is/are TRUE?

$$P:$$ Minimum spanning tree of $$G$$ does not change
$$Q:$$ Shortest path between any pair of vertices does not change

The worst case running times of Insertion sort, Merge sort and Quick sort, respectively, are:

$$G = (V,E)$$ is an undirected simple graph in which each edge has a distinct weight, and e is a particular edge of G. Which of the following statements about the minimum spanning trees $$(MSTs)$$ of $$G$$ is/are TRUE?

$$\,\,\,\,\,\,\,\,\,\,{\rm I}.\,\,\,\,\,\,\,\,\,\,$$ If $$e$$ is the lightest edge of some cycle in $$G,$$ then every $$MST$$ of $$G$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$includes $$e$$
$$\,\,\,\,\,\,\,\,{\rm I}{\rm I}.\,\,\,\,\,\,\,\,\,\,$$ If $$e$$ is the heaviest edge of some cycle in $$G,$$ then every $$MST$$ of $$G$$
$$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$excludes $$e$$

Consider the weighted undirected graph with $$4$$ vertices, where the weight of edge $$\left\{ {i,j} \right\}$$ is given by the entry $${W_{ij}}$$ in the matrix $$W.$$ $$$W = \left[ {\matrix{ 0 & 2 & 8 & 5 \cr 2 & 0 & 5 & 8 \cr 8 & 5 & 0 & X \cr 5 & 8 & X & 0 \cr } } \right]$$$

The largest possible integer value of $$x,$$ for which at least one shortest path between some pair of vertices will contain the edge with weight $$x$$ is _________________.