	Above, we said that a free Boolean algebra is a Boolean algebra with a set of generators that behave a certain way; alternatively, one might start with a set and ask which algebra it generates. Every set "X" generates a free Boolean algebra "FX" defined as the algebra such that for every algebra "B" and function "f" : "X" → "B", there is a unique Boolean algebra homomorphism "f"′ : "FX" → "B" that extends "f". Diagrammatically,