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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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