Three statements are given, followed by four conclusions numbered I, II, III and IV. Assuming the statements to be true, even if they seem to be at variance with commonly known facts, decide which of the conclusions logically follow(s) from the statements.

Statements:

Some desks are trays.

Some trays are plates.

Some plates are desks.

Conclusions:

I. All desks are plates.

II. All plates are desks.

III. Some plates are trays.

IV. All trays are desks.