Unit 3 Part 1 2011 Solutions

# Unit 3 Part 1 2011 Solutions - DERIVATIONS: NATURAL...

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Logic Unit 3 Part 1: Derivations with Negation and Conditional 2011 Niko Scharer 1 DERIVATIONS: NATURAL DEDUCTION Part 1 3.2 E1 Which inference rule justifies the following arguments? (mp, mt, dn or none) a) ~R P ~R P MP b) ~~S T S T NONE! DN cannot be used on a sentential part c) P ~Q Q ~P NONE! First you must use DN, then you can use MT d) (P ~R) ~S ~~S ~(P ~R) MT e) ~(~P Q) P Q None! f) P (P ~P) P P ~P MP g) S R ~P ~S NONE! h) Q (S P) ~ (S P) ~Q MT 3.2 E2 What can you infer (if anything) in one step from the following? What rule of inference are you using? (mp, mt, dn) a) P R ~P ? nothing with MP/MT b) ~~(V W) ~W ? nothing in one step with MP/MT. After DN on the first premise, MT yields ~V. c) ~S ~~T ~S ? ~~T MP d) ~Y ~Z ~Z ? nothing with MP/MT e) P (Q R) ~Q R ? nothing with MP/MT f) P (Q R) ~(Q R) ? ~P MT g) ~~(~P ~~~Q) ? (~P ~~~Q) DN h) ~ Z ~X ? ~~(~Z ~X) DN i) (P Q) R P Q ? R MP j) X ~Y Y ? nothing in one step. After DN on the second premise, MT gets you ~X. k) ~ W (Z ~X) ~~X ? nothing l) (~P R) ~Q ~~Q ? ~(~P R) MT In all of these, you can infer the double negated premises (premise with two ~ in front) with DN. For example, a) ~~(~S ~~T) dn, or ~~~S dn.

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Logic Unit 3 Part 1: Derivations with Negation and Conditional 2011 Niko Scharer 2 3.3 E1: Check the work in the following derivations. Does each line follow from available lines using the rule cited? (a) ~T ~S. R ~~T. S. R 1 Show ~R ERROR. show line incorrect 2 S pr3 3 ~T ~S pr1 4 T 2 3 mt ERROR. You need the negated consequent to use MT. 5 R ~~T pr2 6 R T 5 dn ERROR. dn cannot be used on a sentential component. 7 R 4 6 mp ERROR. mp moves from a conditional and the antecedent to the consquent. 8 7 dd This cannot be fixed. It is not valid, so the conclusion cannot be derived from the premises.
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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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Unit 3 Part 1 2011 Solutions - DERIVATIONS: NATURAL...

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