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Propositional logic question

  1. Feb 16, 2015 #1
    1. The problem statement, all variables and given/known data
    For each of the premise-conclusion pairs below, give a valid step-by-step argument ( proof ) along with the name of the inference rule used in each step

    premise { ¬ p → r ∧ ¬ s , t → s , u → ¬p , ¬w , u ∨ w } conclusion : ¬t ∨ w
    2. Relevant equations

    All the inference rules, Modus ponens, Modus tollens, etc...
    3. The attempt at a solution

    I tried by using the w term but it didn't work so I did this:

    1) u → ¬ p Prmise
    2) ¬p → r ∧ ¬s ass
    3) u → r ∧ ¬ s

    However I seem stuck
     
  2. jcsd
  3. Feb 16, 2015 #2

    Svein

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    1. u⇒¬ p
    2. ¬ p⇒r ∧ ¬ s
    3. ∴u ⇒ r ∧ ¬ s
    4. t⇒s
    5. ∴¬ s⇒¬ t
    6. u ∨ w
    7. ¬w
    8. ∴u
    9. ∴r ∧ ¬ s
    10. ∴¬ s
    11. ∴¬ t
    12. ¬w
    13. ∴¬t ∨ w
     
  4. Feb 16, 2015 #3
    you're allowed to re-use ¬w>?
     
  5. Feb 16, 2015 #4

    Svein

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    Science Advisor

    Why not? A premise is a premise.
     
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