Intro to Logic HW3

Intro to Logic HW3 - HW#3 Wednesday, July 25, 2007 10:10 AM...

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Unformatted text preview: HW#3 Wednesday, July 25, 2007 10:10 AM For each of the following arguments, construct a derivation of the conclusion from the premises, using the inference rules of System SL. 1 P v Q R ; P T ; Q & U R ; ~T / U 1 2 3 4 5 6 7 8 9 10 11 12 P v Q R Pr P T Pr Q& U R Pr ~T Pr SHOW: U DD ~P 2,4, O Q R 1,6,vO Q 3,&O R 7,8, O U R 3,&O R U 10, O U 9,11, O 2 ~P v Q ; Q&R 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 S ; ~T ~S / P&R T ~P v Q Pr Q&R S Pr ~T ~S Pr SHOW: P&R T CD P&R As SHOW: T DD P 5,&O ~~P 7,DN Q 1,8,vO R 5,&O Q&R 9,10,&I Q&R S 2, O S 11,12, O ~~S 13,DN ~~T 3,14, O T 15,DN 3 P Q S ; S v T R / Q P R 1 2 3 4 5 6 7 P Q S Pr S v T R Pr SHOW: Q P R CD Q As SHOW: P R CD P As SHOW:R DD Intro to Logic Page 1 8 9 10 11 Q S 1,6, O S 4,8, O S v T 9,vI R 2,10, O 4 P Q v R ; P ~Q ~R ; P ~Q / ~P 1 2 3 4 5 6 7 8 9 10 11 12 P Q v R Pr P ~Q ~R Pr P ~Q Pr SHOW: ~P ID P As SHOW: X DD Q v R 1,5, O ~Q 3,5, O ~Q ~R 2,5, O R 7,8,vO ~R 8,9, O X 10,11,XI 5 P ~T Q ; T R / P Q v P R 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 P ~T Q Pr T R Pr SHOW: P Q v P R ID ~ P Q v P R As SHOW:X DD ~ P Q 4,~vO ~ P R 4,~vO P&~Q 6,~ O P&~R 7,~ O ~Q 8,&O ~ P ~T 1,10, O ~P ~T 11,~ O ~T ~P 12, O P 8,&O ~~P 14,DN ~~T 13,15, O T 16,DN T R 2, O R 17,18, O ~R 9,&O X 19,20,XI Intro to Logic Page 2 Intro to Logic Page 3 ...
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