Let G be a weighted connected graph

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

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$)$ None of the above