Three statements are given, followed by three conclusions numbered I, II and III. 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:

No carrots are beets.

Some carrots are gingers.

Some gingers are beets.

Conclusions:

I. All beets are gingers.

II. Some gingers are carrots.

III. Some beets are carrots.