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:
Some pineapples are oranges.
All oranges are bananas.
All bananas are plums.

Conclusions:
I. Some pineapples are plums.
II. All oranges are plums.
III. No pineapple is a banana.