Homework+5+answers

Homework+5+answers - T ; Q --> ~ T ; ~Q...

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Homework For Monday 21st February: ANSWERS Show that the following arguments are valid using direct derivation : (1) (P v Q) --> R ; Q ; Q --> T / R & T (1) (P v Q) --> R Pr (2) Q Pr (3) Q --> T Pr (4) SHOW: R & T DD (5) | T 2,3,-->O (6) | P v Q 2,vI (7) | R 1,6,-->O (2) P <--> R ; ~P ; ~ ~S v R / S (1) P <--> R Pr (2) ~P Pr (3) ~~S v R Pr (4) SHOW: S DD (5) | R-->P 1,<-->O (6) | ~R 2,5,-->O (7) |~~S 3,6,vO (8) |S 7,DN (3)
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Unformatted text preview: T ; Q --&amp;gt; ~ T ; ~Q --&amp;gt; R / R v U (1) T Pr (2) Q --&amp;gt; ~ T Pr (3) ~Q --&amp;gt; R Pr (4) SHOW: R v U DD (5) | ~~T 1,DN (6) | ~Q 2,5,--&amp;gt;O (7) | R 3,6,--&amp;gt;O (8) | R v U 7, v I (4) P --&amp;gt; (Q --&amp;gt;R) ; Q --&amp;gt; (R--&amp;gt;Q) ; P &amp;amp; Q / Q &amp;lt;--&amp;gt; R (1) P --&amp;gt; (Q --&amp;gt;R) Pr (2) Q --&amp;gt; (R--&amp;gt;Q) Pr (3) P &amp;amp; Q Pr (4) SHOW: Q &amp;lt;--&amp;gt; R DD (5) | P 3,&amp;amp;O (6) | Q--&amp;gt;R 1,5,--&amp;gt;O (7) | Q 3,&amp;amp;O (8) | R--&amp;gt;Q 2,7,--&amp;gt;O (9) | Q &amp;lt;--&amp;gt; R 6,8,&amp;lt;--&amp;gt;I...
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