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The only way I know of that can give you ¬B is to use negation introduction. If you can't follow this year's textbook, go back to the textbook from COS161 (Gutenplan), it's expained much better there.
Negation introduction (reductio ad absurdum) basically relies on you to assert something. If that assertion causes a contradiction somewhere down the line, your original assertion must be false, and the negation of your assertion therefore must be true.