Any help would be appreciated, thank you
Proof: Let $G$ be a 2-connected graph and $u$, $v$ be two non-adjacent vertices in $G$. Show there must be at least two intern ally-disjoint paths between $u$ and $v$.
A minimal 2-connected graph is a cycle $C_{k}$ where $k\in \mathbb N$, $k≥3$, then $\forall u,v\in V(C_{k})$, we have two distinct paths because $\forall v\in V(C_{k})$, $deg(v)≥2$. Then, it must be the case that there are at least 2 distinct paths between $u,v\in V(G)$ where $G = (V,E)$ and $G$ is 2-connected. Therefore, claim must hold.