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Laws of , , and Excluded middle law Contradiction law P P T P P F NameLaw Identity laws P F P P T P Domination laws P T T P F F Idempotent laws P P P P P P Double-negation law ( P) P

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Commutative laws P Q Q P P Q Q P NameLaw Associative laws (P Q) R P (Q R) (P Q) R P (Q R) Distributive laws (P Q) (P R) P (Q R) (P Q) (P R) P (Q R) De Morgan’s laws (P Q) P Q (P Q) P Q Absorption laws P (P Q) P P (P Q) P

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Laws of and Implication Law P Q P Q NameLaw Equivalence Law P Q P Q Q P Contrapositive Law P Q Q P P Q P Q F Contradiction Law

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Main Rules of Inference A, B |= A B Law of combination A B |= B Law of simplification A B |= A Variant of law of simplification A |= A B Law of addition B |= A B Variant of law of addition A, A B |= B Modus ponens B, A B |= A Modus tollens A B, B C |= A C Hypothetical syllogism A B, A |= B Disjunctive syllogism A B, B |= A Variant of disjunctive syllogism A B, A B |= B Law of cases A B |= A B Equivalence elimination A B |= B A Variant of equivalence elimination A B, B A |= A B Equivalence introduction A, A |= B Inconsistency law

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