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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
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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) ......
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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)
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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)
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