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Math Help - Demonstration, please help.

  1. #1
    Member
    Joined
    Mar 2010
    Posts
    75

    Demonstration, please help.

    Premises:
    a)~p v q -> r
    b) s v ~q
    c)~t
    d)p -> t
    e)~p (and) r -> ~s
    Therefore, ~q



    This is my attempt:

    1) ~t (from c)

    2) p-> t
    ~t
    therefore, ~p (Modus Tollens)

    3)~p v q-> r
    ~p
    therefore, r (Whats is this called? elimination?)

    4)~p (and) r-> ~s
    ~p (and) r (<---from 2, 3)
    therefore, ~s (<--Modus Ponens)

    5) s v ~q
    ~s (from 4)
    therefore, ~q (elimination)


    Did I do good? Is there anything I should add/ change?
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  2. #2
    Member
    Joined
    Mar 2010
    Posts
    75
    Also, If I am working on a demonstration and the conclusion is an 'or statement' such as: ~p OR q

    and I have proven that ~p, then does that means that I have completed my proof...? How would I write that as a step in the demonstration? b/c I am not suppose to use the conclusion as part of my proof. So once I reach the part of the proof where ~p, that is part of my conclusion, since (conclusion: ~p OR q). So am I done once I reach either ~p or q?

    For example (conclusion: ~p OR t):
    p OR q
    ~q
    therefore, ~p
    (would I add a separate step for the conclusion, or add another line here and write therefore AGAIN and then write ~p or t, since the conclusion is reached...??)
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