3 & 4. The fallacies of composition and division occur when the properties of parts and composites are mistakenly thought to be transferable from one to the other. Consider the two sentences: Every member of the investigative team was an excellent researcher. It was an excellent investigative team. Here it is ‘excellence’ that is the property in question. The fallacy of composition is the inference from (a) to (b) but it need not hold if members of the team cannot work cooperatively with each other. The reverse inference from (b) to (a)—the fallacy of division—may also fail if some essential members of the team have a supportive or administrative role rather than a research role. - http://plato.stanford.edu/entries/fallacies/