Correct option is A

I. Some ceilings being dogs is a possibility. (True, there is no relation is given between them, so can say that in possibility only)
II. No dog is an apple. (True, all dogs are beds and bed is coverage of dogs, and no beds are apple is given so this is true )
III. All beds are dogs. (False, can not say in definite because this is not given)
IV. No ceiling is an apple. (False, some ceilings are not apples which is comes in beds but we have no information about remaining ceilings so we cannot say this for whole ceilings)
Only (I)and (II) is true.