Derivation Exercises Unit 3 part 1 Selected Answers Q 20+

Derivation Exercises Unit 3 part 1 Selected Answers Q 20+ -...

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Derivation Exercises for Unit 3 Part 1: Derivations with Conditional and Negation © Niko Scharer 1 Derivations Exercises Unit 3 Part 1 Derivations with NEGATION and CONDITIONAL SELECTED ANSWERS QUESTIONS 20-70 Answers only for selected derivations. In the annotations: conc= conclusion, ant= antecedent, cons=consequent, cond=conditional Use any derivation method (DD, CD, ID) and any rule (MP, MT, DN and R). 20. R ~ R . ~R 1 Show ~R show conc 2 R ass id you can’t show ~R directly, so assume the opposite goal: a contradiction 3 ~R pr1 2 mp use your assumption! 4 2 3 id lines 2 and 3 contradict each other. The indirect derivation is complete. Box and cancel. 21. P Q. ~P Q. Q 1 Show Q show conc 2 ~Q ass id you can’t show Q directly, so assume the opposite goal: a contradiction 3 ~P 2 pr1 mt use your assumption! 4 ~~P 2 pr2 mt use your assumption again! 5 3 4 id lines 3 and 4 contradict each other. ID is done. Box and cancel. 24. ~~R ~~T . ~T ~R 1 Show ~T ~R show conc 2 ~T ass cd assume the ant. of 1; goal: cons. of 1: ~R 3 ~~~T 2 dn 4 ~~~R 3 mt 5 ~R 4 dn cd derived cons. of 1. CD done. Box & cancel
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Derivation Exercises for Unit 3 Part 1: Derivations with Conditional and Negation © Niko Scharer 2 26. ~P. P (R S) 3 solutions given. All involve ID. Once you uncover a contradiction, you can prove anything! Here the antecedent of the conclusion contradicts the premise. If two available lines contradict each other, put in a show line for what you need, then assume the opposite and reiterate the contradictory lines (to get them under your assumption and show line). 1 Show P (R S) show conc 2 P ass cd Show line 1 is a cond. Assume ant. New goal: the consequent: R S 3 show R S Show consequent! 4 R ass cd Show line 3 is a cond. Assume ant. New goal: the consequent: S 5 Show S Show consequent! 6 ~S ass id Can’t show S directly, so ass opposite for ID 7 P 2 r line 2 contradicts the premise. Get them 8 ~P pr1 both under show line 5! 9 7 8 id ID done. Box back to 6 and cancel 5. 10 5 cd Line 5 is the cons. of cond. 3. CD done. Box back to 4 and cancel 3. 11 3 cd Line 3 is cons. of 1. CD done. Box & cancel ~P P (R S) 1 Show P (R S) show conc 2 P ass cd Show line is a cond. Assume ant. Goal: R S Line 2 contradicts pr1. You can prove anything!
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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- Toronto.

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Derivation Exercises Unit 3 part 1 Selected Answers Q 20+ -...

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