Rules and Laws

Rules and Laws - Is it possible to reduce even further?...

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Discussion #11 Chapter 1, Section 6.1-5 1/16 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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Discussion #9 Chapter 1, Section 4 2/16 Logical Equivalence Leading to Reductions We can reduce  and  to , , and  by: P  Q (P  Q)  (Q  P) P  Q P  Q We now only need , , and .
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Unformatted text preview: Is it possible to reduce even further? Discussion #10 Chapter 1, Section 5 3/19 Laws of , , and Excluded middle law Contradiction law P P T P P F Name Law 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 Discussion #10 Chapter 1, Section 5 4/19 Commutative laws P Q Q P P Q Q P Name Law 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 Morgans laws (P Q) P Q (P Q) P Q Absorption laws P (P Q) P P (P Q) P...
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Rules and Laws - Is it possible to reduce even further?...

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