I have been told that with the conjunction "or" we must apply the following rule: a singular verb is used if the subject that comes after "or" is singular. Is it correct?

I would naturally say the apple or the orange *is* good. But it seems that we should also say 

* the apples or the orange ***is*** good
* but the orange or the apples ***are*** good.

Is it correct?

Otherwise, if I am thinking of "this or that or both", is it correct to use the plural? And say the apple or the orange ***are*** (both) good.