SOLUTION: how do you construct a proof for the following arguments? Help on homework s V p p → ( a →~b) ~(w→s) r→~(b→~a) ___________ _________ ~r

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Question 1061930: how do you construct a proof for the following arguments? Help on homework
s V p
p → ( a →~b)
~(w→s)
r→~(b→~a)
_____________________
~r

Answer by solver91311(24713)   (Show Source): You can put this solution on YOUR website!


 1.   S v P

 2.   P -> (A -> B)

 3.   ~(W -> S)

 4.   R -> ~(B -> ~A)     :.    ~R

===================================

 5.   ~(~W v S)           3: Material Implication

 6.   W & ~S              5: De Morgan

 7.   ~S                  6: Conjunctive Elimination

 8.   P                   7, 1:  Disjunctive Syllogism

 9.   A -> ~B             8, 2:  Modus Ponens

10.   ~A v ~B             9: Material Implication

11.   ~B v ~A            10: Commutativity

12.   B -> ~A            11: Material Implication

13.   ~(~(B -> ~A))      12: Double Negation Introduction

13.   :. ~R              13, 4: Modus Tolens

John

My calculator said it, I believe it, that settles it
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