Logic, the book is modern logic by Graeme Forbes. Chapter 4 page 108 questions 5,6,7, and 9

108 Chapter 4: Natural Deduction in Sentential Logic tive, it is likely that its role in the proof will be to be one ofa of contradictory formulae in an application of E. You should the fore consider trying to derive the formula within the scope of . If one of your premises or assumptions has ~'as its main If you are trying to deduce a sentence-letter and there is no obvio use DN. Any double negation has as its main connective. N , to get the other member of the contradictory pair. rive its double negation and th At this point in the development of NK, you should only assume formula p if you are trying to deduce its negation or trying to dedu a conditional with p as antecedent. A common beginner's error is t make assumptions just for the sake of being able to apply an E-rul (particularly -E). At this stage, only make an assumption when you refer to the first point in this list. have reasoned how you will use ~I or -I to discharge it. Exercises Show the following ("p -NK q, abbreviates p-NK q and q-NK p'): (6) (A & B),A NK B (7) A N~(B & (A & B) (9) B (A & ~A)-NK-B (11) (A & B)--A-NK A--B (12) (A & ~B)-B-NK A B "(13) A B, B -A-NK-A (15) A~(B & C), B CH-NK A A&B) (17)-NK (-A A) A "(18) (A & ~B)--A-NK A B 108 Chapter 4: Natural Deduction in Sentential Logic tive, it is likely that its role in the proof will be to be one ofa of contradictory formulae in an application of E. You should the fore consider trying to derive the formula within the scope of . If one of your premises or assumptions has ~'as its main If you are trying to deduce a sentence-letter and there is no obvio use DN. Any double negation has as its main connective. N , to get the other member of the contradictory pair. rive its double negation and th At this point in the development of NK, you should only assume formula p if you are trying to deduce its negation or trying to dedu a conditional with p as antecedent. A common beginner's error is t make assumptions just for the sake of being able to apply an E-rul (particularly -E). At this stage, only make an assumption when you refer to the first point in this list. have reasoned how you will use ~I or -I to discharge it. Exercises Show the following ("p -NK q, abbreviates p-NK q and q-NK p'): (6) (A & B),A NK B (7) A N~(B & (A & B) (9) B (A & ~A)-NK-B (11) (A & B)--A-NK A--B (12) (A & ~B)-B-NK A B "(13) A B, B -A-NK-A (15) A~(B & C), B CH-NK A A&B) (17)-NK (-A A) A "(18) (A & ~B)--A-NK A B