A$9-2.$ Matchings and covers

Let $G$ be a connected graph with at least one edge.

$($a$)$ Let $G$ be a graph that has a perfect matching $($note that there may be multiple perfect matchings in $G.$ Prove that if a bridge $e$ is in one perfect matching of $G,$ then $e$ is in every perfect matching of $G.$

$($b$)$ Prove or disprove: Every vertex of $G$ is saturated by some maximum matching of $G.$

$($c$)$ Prove or disprove: Every vertex of $G$ is in some minimum cover of $G.$