Boolean Algebra

Inference Rules

Modus Ponens: $ P \rightarrow Q, P \vdash Q. $

Modus Tollens: $ P \rightarrow Q, \neg Q \vdash \neg P. $

Or Introduction: $ P \vdash (P \lor Q). $

And Introduction: $ P, Q \vdash (P \land Q). $

And Elimination: $ (P \land Q) \vdash P, Q. $

Material Implication: $(P \rightarrow Q) \vdash (\neg P \lor Q). $