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:
All apples are bananas.
All grapes are bananas.
All bananas are nuts.

Conclusions:
I. All apples are nuts.
II. All grapes are nuts.
III. No nuts are bananas.