1 CA 208 Logic Ex4 Commutativity (P  Q) ................. Associativity P  (Q  R)  (P  Q)  R Distributivity P  (Q  R) .................. Idempotency.

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Presentation transcript:

1 CA 208 Logic Ex4 Commutativity (P  Q)  Associativity P  (Q  R)  (P  Q)  R Distributivity P  (Q  R)  Idempotency (P  P)  P Absorption (P  T)  Commutativity (P  Q)  (Q  P) Associativity: P  (Q  R)  Distributivity P  (Q  R)  (P  Q)  (P  R) Idempotency (P  P)  Absorption (P   )  P

2 CA 208 Logic Ex4 De Morgan  (P  Q)  Double Negation   P  The Falsum/Absurd:  (P   P)   De Morgan  (P  Q)  (  P   Q) The Verum/True: T (P   P) ......

3 CA 208 Logic Ex4 Given our definition of the syntax of propositional logic, which of the following are formulas of propositional logic and which are not (and why)? A  A  A  (  A)  A  A  AA A  B (A  B) ((A  B)) A  B  C (A  B)  C ((A  B)  C)  C (  C) 

4 CA 208 Logic Ex4 Prove the following in the natural deduction calculus (proof system): {A,B} |- (B  A) {A,B} |- (A  A) {A,B} |- ((A  B)  C) {(A  B),(B  C)} |- C {(C  B), (B  A)} |- (C  A) {A, (A  (B  C)), (C  (D  E)), (B  (F  E))} |- E {A, ((B  A)  C), (C  E)} |- E {} |- (C  C)