CPSC 125 Ch 1 sec 2

Propositional Logic ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Valid Argument ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Valid Argument ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Rules for Propositional Logic ,[object Object],Work only in one direction Truth preserving rules Allows new wffs to be derived Allows individual wffs to be rewritten Inference Rules Equivalence Rules

Equivalence Rules ,[object Object],[object Object],[object Object],Equivalance - equ (P  Q) Λ ( Q  P) P  Q Double Negation- dn (R  )  R implication - imp R  V S R  S De-Morgan’s Laws De-Morgan R  Λ S  R  V S  (R V S)  (R Λ S)  Associative- ass R Λ (S Λ Q) R V (S V Q) (R V S) V Q (R Λ S) Λ Q Commutative - comm S V R R V S Abbreviation for rule Equivalent to Expression

Inference Rules ,[object Object],[object Object],Addition- add R V S R Simplification- sim R, S R Λ S Conjunction-con R Λ S R, S Modus Tollens- mt R  R  S, S  Modus Ponens- mp S R, R  S Abbreviation for rule Can Derive From

Examples ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Deduction Method ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

More Inference Rules ,[object Object],Distributive - dist (P V Q) Λ (P V R) P V (Q Λ R) Distributive - dist (P Λ Q) V (P Λ R) P Λ (Q V R) Inconsistency - inc Q P, P  Exportation - exp P  (Q  R) (P Λ Q)  R Self-reference - self P P V P Self-reference - self P Λ P P Contraposition- cont P  Q Q   P  Contraposition- cont Q   P  P  Q Disjunctive syllogism- ds Q P V Q, P  Hypothetical syllogism- hs P  R P  Q, Q  R Name / Abbreviation Can Derive From

Proofs of inference rules ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Proofs using Propositional Logic ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

More Proofs ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Proof Continued ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Proving Verbal Arguments ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Verbal Argument Proof ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

Class Exercise ,[object Object],[object Object],[object Object],[object Object],[object Object]

Class Exercise ,[object Object],[object Object]

CPSC 125 Ch 1 sec 2

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CPSC 125 Ch 1 sec 2