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Sentential calculus q

  1. Jan 23, 2007 #1

    Using sentential calculus (with a four column format), prove that the conclusion (s ^ ~p) ==> t follows from the premises: ~(q ^ s) and q OR p. (Hint: Employ conditionalization).

    Work done:
    Code (Text):

       (1)  ~(q ^ s)         P
       (2)  (~q OR ~s)     DeM (1)
       (3)  q OR p            P
       (4)  p OR ~s          Cut (2, 3)
       (5)  ~(s ^ ~p)       DeM (4)
    but, of course I'm to show (s ^ ~p) ==> t.

    How should I go about it? thank you.
  2. jcsd
  3. Jan 23, 2007 #2
    contrapositive of the hypothesis seems to work! :-)
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