Let G be a weighted connected graph $2\mathrm{.}5$

I. If the edge weights are all different G must have exactly one MST

II$.$ If the edge weights are not all different G must have more than one MST

III. If the edge weights are all same, every spanning tree of G is a MST

Which one of the following is correct$$

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

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

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

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

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