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Using inference rules/equivalences

  1. Dec 9, 2015 #1
    1. The problem statement, all variables and given/known data
    Using[/PLAIN] [Broken] inference rules/equivalencies, Show that
    ( ( (¬ A ∨ ¬ B ) → ( C ∧ D ) ) ∧ ( C → E) ∧ ( ¬ E )) → A


    2. Relevant equations
    ( ( (¬ A ∨ ¬ B ) → ( C ∧ D ) ) ∧ ( C → E) ∧ ( ¬ E )) → A


    3. The attempt at a solution

    Using inference rules/equivalencies, Show that
    ( ( (¬ A ∨ ¬ B ) → ( C ∧ D ) ) ∧ ( C → E) ∧ ( ¬ E )) → A

    This is my answer.
    Consider about,
    ( (¬ A ∨ ¬ B ) → ( C ∧ D ) ) ∧ ( C → E) ∧ ( ¬ E )
    Then,
    ( (¬ A ∨ ¬ B ) → ( C ∧ D ) ) ∧ ¬ E
    ( ¬( A ∧ B ) → ( C ∧ D ) ) ∧ ¬ E
    ( ¬¬( A ∧ B ) ∨ ( C ∧ D ) ) ∧ ¬ E
    ( ( A ∧ B ) ∨ ( C ∧ D ) ) ∧ ¬ E
    After that, I cannot reach the answer → A
     
    Last edited by a moderator: May 7, 2017
  2. jcsd
  3. Dec 9, 2015 #2

    RUber

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    To make sure I am reading this right, I will use English connectors.
    [ (not A or nor B ) implies (C and D) ] and [( C implies E ) and (not E) ].
    The right side simplifies to (not C) and (not E), not just (not E) like you have.
    Having the not C will help you conclude that A must be true.
     
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