Fallacy of composition:
Arises when one infers that something is true of the whole from the fact that it is true of some part of the whole (or even of every proper part). For example: "This wheel is made of rubber, therefore the vehicle to which it is a part is also made of rubber." This is clearly fallacious, because vehicles are often made with a variety of parts, many of which may not be made of rubber.
Fallacy of division:
Occurs when one reasons logically that something true for the whole must also be true of all or some of its parts.
YOU ARE READING
Idioms, Fallacies, and Paradoxes
RandomAll definitions are 100% written by Wikipedia, not my own words.