I would rather X I´d prefer

Would you prefer to take a video or an art class?

a- I´d prefer studying video to learning about art.

b - I´d prefer to study video.

c- I´d prefer studying video.


Which answer is correct? (a,b or c?) I ask this because in Murphy´s "grammar in use" he says that the answer for the question - "should we take the train? is - "No, I´d prefer to drive" and not "I´d prefer driving."


Can I say - " I´d prefer to stay home tonight than to go out" and "I´d prefer to stay home tonight than go out" - or should I say- "I´d prefer to stay home tonight rather than go out"? -

Thanks for your help.