Let G be a weighted connected graph

I. If e is a minimum$-$weight edge in G$,$ it must be contained in a MST$.$

II$.$ If e is a minimum$-$weight edge in G$,$ it must be contained in each MST$.$

III. If e is a maximum$-$weight edge in G$,$ it must not be contained in any MST$.$

Which one of the following is correct$$

$[$ A $]$ I and III are true, II is false

$[$ B $]$ I and II and III are true

$[$ C $]$ I and II and III are false

$[$ D $]$ II and III are true but I is false

$[$ E $]$ I is true but II and III are false