Q31

Let $G(V, E)$ be an undirected, edge-weighted graph with integer weights. The weight of a path is the sum of the weights of the edges in that path. The length of a path is the number of edges in that path. Let $s \in V$ be a vertex in $G$. For every $u \in V$ and for every $k \geq 0$, let $d_{k}(u)$ denote the weight of a shortest path (in terms of weight) from $s$ to $u$ of length at most $k$. If there is no path from $s$ to $u$ of length at most $k$, then $d_{k}(u)=\infty$. Consider the statements: S1: For every $k \geq 0$ and $u \in V, d_{k+1}(u) \leq d_{k}(u)$. S2: For every $(u, v) \in E$, if $(u, v)$ is part of a shortest path (in terms of weight) from $s$ to $v$, then for every $k \geq 0, d_{k}(u) \leq d_{k}(v)$. Which one of the following options is correct?