What are the fallacies of composition and division (and how does hasty generalization differ)?

Composition: what's true of the parts must be true of the whole. Division: the reverse. Hasty generalization: leaping to a rule from too few cases.

• Fallacy of composition — assuming a property of the parts automatically transfers to the whole. "Each player is excellent, so the team must be excellent." (Great individuals can still make a poor team.)
• Fallacy of division — the reverse: assuming a property of the whole transfers to each part. "This is a brilliant orchestra, so every musician in it is brilliant."
• Hasty generalization — drawing a broad conclusion from a sample that's too small or unrepresentative. "Two rude waiters here, so this whole city is rude."

Composition and division are about part ↔ whole transfer in either direction; hasty generalization is about sample → population with insufficient evidence. All three over-extend from limited information — but composition/division mistake structure, while hasty generalization mistakes quantity of evidence.

Tip: Composition = parts up to whole; Division = whole down to parts. Hasty generalization is a different error — too few examples, not a part/whole mix-up.