Proving (s ^ ~p) ==> t using Sentential Calculus

[lizzyb]

Question:

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:

   (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.

 

[lizzyb]

contrapositive of the hypothesis seems to work! :-)