Problem $1.(10$ points$)$ Let $G=(V,E)$ be a directed graph and assume there exists a node vinV such that for every uin$\frac{V}{\frac{?}{?}}\{v\},$ there is a directed path from $v$ to $u$ in $G.$ Prove whether the following statements are true or false:

Statement $1$: $G$ has one weakly connected component.

Statement $2$: $G$ has one strongly connected component.Problem $1.(10$ points$)$ Let $G=(V,E)$ be a directed graph and assume there exists a node vinV such that for every uin$\frac{V}{\frac{?}{?}}\{v\},$ there is a directed path from $v$ to $u$ in $G.$ Prove whether the following statements are true or false:

Statement $1$: $G$ has one weakly connected component.

Statement $2$: $G$ has one strongly connected component.