Derivation Exercises Unit 3 Part 1 Answers 1-19

# Derivation Exercises Unit 3 Part 1 Answers 1-19 -...

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Derivations Exercises 1 Derivations with NEGATION and CONDITIONAL ANSWERS QUESTIONS 1-19 I have included all the answers for the first two sections. After that, there will be answers only for selected derivations. For the first set, use Direct Derivation only (also MP, MT, DN and R). Do not use ID or CD. 1. R. R S. S T. T 1 Show T show conc First line is always a show line. 2 R PR 1 Indent after a show line 3 R S PR 2 4 S T PR 3 5 S 2 3 MP Line 2 gives the antecedent of line 3 6 T 4 5 MP Line 5 gives the antecedent of line 4 7 6 dd Line 6 is the sentence on the show line, derived directly. Box and cancel show (strike through) 2. T W. W X. ~X. ~T 1 Show ~T First line is always a show line. 2 T W PR 1 3 W X PR 2 4 ~X PR 3 5 ~W 4 3 MT Line 4 is the negation of the consequent on line 3 6 ~T 5 2 MT Line 5 is the negation of the consequent on line 2 7 6 DD Line 6 is the sentence on the show line, derived directly. Box and cancel show (strike through) 3. ~~P. ~~(P Q). ~~Q 1 Show ~~Q show conc First line is always a show line. 2 P PR 1 DN I don’t have to list the premises, I can just refer to them. Line 2 is the double negated first premise. 3 P Q PR 2 DN Now I am using DN on the second premise 4 Q 2 3 MP Line 2 is the antecedent of line 3 5 ~~Q 4 DN I have to double negate line 4 to reach my goal. 6 5 DD Line 5 is the sentence on the show line, derived directly. Box and cancel. Derivation Exercises for Unit 3 Part 1: Answers for Q1-19 © Niko Scharer 1

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4. P (R S). P. ~S. ~R 1 Show ~R show conc First line is always a show line. 2 R S pr1 pr2 mp 3 ~R pr3 2 mt 4 3 dd dd done on 3. Box and cancel. 5. (P S) Q. (R T) ~Q. P S. ~(R T) 1 Show ~(R T) show conc First line is always a show line. 2 Q pr3 pr1 mp pr3 is the antecedent of the first premise. 3 ~~Q 2 dn double negate line 2 so that it is the negation of the consequent of premise 2. 4 ~(R T) 3 pr2 mt 3 is the negation of the cons. of pr2, use MT to get the negation of the antecedent. 5 4 dd Box and cancel. 6.
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## This note was uploaded on 02/01/2012 for the course PHL PHL245 taught by Professor Scharer during the Winter '11 term at University of Toronto.

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Derivation Exercises Unit 3 Part 1 Answers 1-19 -...

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