 In LT Boole gave detailed instructions on how to use his algebra to obtain valid propositional conclusions from propositional premises about classes when the propositions were universal. (He avoided particular propositions until Chapter XV, the last chapter of  LT on logic.) He showed how to express English language propositions as equations, the steps needed to obtain desired conclusion equations, and how they are to be interpreted as conclusion propositions to the premises. The algebraic steps can be lengthy and he gave some shortcuts in Chapter IX, but we now know that any method to carry out such deductions will confront a complexity of computation that grows rapidly with the number of propositional variables. 