# Homework+6+Answers - | ~Q 1&O(9 | | X 7,8,XI(3 ~R> S...

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Homework 6: Bring to Class on Monday Feb 28th Do the following derivations: (1) P <--> Q ; ~R --> P / ~Q --> R (1) P <--> Q Pr (2) ~R --> P Pr (3) SHOW: ~Q --> R CD (4) | ~Q As (5) | SHOW: R DD (6) | | P --> Q 1,<-->O (7) | | ~P 4,6,-->O (8) | | ~~R 2,7,-->O (9) | | R 8, DN Note that I can also SHOW: R (line 5) by using ID instead of DD e.g. (1) P <--> Q Pr (2) ~R --> P Pr (3) SHOW: ~Q --> R CD (4) | ~Q As (5) | SHOW: R ID (6) | | ~R As (7) | | SHOW: X DD (8) | | | P 2,6, -->O (9) | | | P-->Q 1,<-->O (10) | | |Q 7,8,-->O (11) | | |X 4,10,XI (2) P & ~Q ; R v Q / ~ (P & ~R ) Pr (2) R v Q Pr (3) SHOW: ~ (P & ~R) ID As (5) | SHOW: X DD (6) | | ~R (7) | | Q 2,6,vO (8) |

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Unformatted text preview: | ~Q 1,&O (9) | | X 7,8,XI (3) ~R --> S ; S --> T / S v (R v T) (1) ~R --> S Pr (2) S --> T Pr (3) SHOW: S v (R v T) ID (4) |~[S v (R v T)] As (5) |SHOW: X DD (6) | |~S 4,~vO (7) | | ~(R v T) 4,~vO (8) | | ~R 7,~vO (9) | | S 1,8,-->O (10) | | X 6,9,XI Notice that in this derivation I don't need to use premise 2 at all (though I could use it if I wanted to). (4) / Q --> ~ (P & ~Q) [there is no premise, so your first line in a show line in this problem] (1) SHOW: Q--> ~(P & ~Q) CD (2) | Q As (3) | SHOW: ~(P & ~Q) ID (4) | | P & ~Q As (5) | | SHOW: X DD (6) | | |~Q 4,&O (7) | | | X 2,6,XI...
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Homework+6+Answers - | ~Q 1&O(9 | | X 7,8,XI(3 ~R> S...

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