layman_ch08 - CHAPTER 8 Statement Logic: Proofs The starred...

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98 SOLUTIONS MANUAL CHAPTER 8 Statement Logic: Proofs The starred items are also contained in the Answer Key in the back of The Power of Logic . Exercise 8.1 Part A: Annotating These proofs use only the first eight rules of inference, the implicational rules given in Section 8.1. *1 . 1 . F G 2 . G H F H 3 . F H 1, 2, HS 2 . 1 . ~ S ~P 2 . ~ S K ~P 3 . ~ P 1 , 2 , M P 4 . K ~P 3, Add 3 . 1 . E (T S) 2 . ~ ( T S) 3 . ~ R E ~R 4 . ~ E 1 , 2 , M T 5 . ~ R 3 , 4 , D S *4 . 1 . H ~C 2 . H ~B 3 . ~ C D 4 . ( ~
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C H A P T E R 8 : S T A T E M E N T L O G I C : P R O O F S 9 9 *7 . 1 . ~ ( P Q) R 2 . ( ~ E ~R) (A B) 3 . E (P Q) 4 . ~ R B (F G) 5 . ~ ( P Q) 1, 4, DS 6 . ~ E 3 , 5 , M T 7 . ~ E ~R 4, 6, Conj 8 . A B 2, 7, MP 9 . B 8 , S i m p 1 0 . B (F G ) 9, Add 8 . 1 . F S 2 . G 3 . [ G (F S)] ~T 4 . ~ B T ~~B 5 . G (F S) 1, 2, Conj 6 . ~ T 3 , 5 , M P 7 . ~ ~ B 4 , 6 , M T 9 . 1 . F B 2 . ~ D 3 . ( ~ D G) (B S) 4 . G 5 . ~ S
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100 SOLUTIONS MANUAL 14. Add 15. MT * 1 6 . Incorrect. This is not CD. To have CD, the disjuncts of the disjunctive premise must be antecedents of the conditional premises. (This is a valid argument, however, and it is of a form that is sometimes called “destructive dilemma” and that is sometimes included in sets of rules of inference by other authors.) 17. In co r
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layman_ch08 - CHAPTER 8 Statement Logic: Proofs The starred...

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