Eight people A, B, C, D, E, F, G and H live in a four-storey building. The…

Eight people A, B, C, D, E, F, G and H live in a four-storey building. The ground floor is numbered 1 and the top floor is numbered 4. Each floor has two flats: flat P in the west and flat Q in the east.

C does not live on an odd-numbered floor. B lives to the south-east of A. There is exactly one floor gap between A and G, and G lives to the east of C.

H lives below B in the same named flat. F lives to the north of E in the same named flat.

Which of the following statements are true? I. A lives on the topmost floor. II. G and C live on the same floor. III. No one lives to the west of E.