SOLUTION: Determine if the given argument is valid or not: P -> Q R -> S ~ Qv ~ S (the 3 dots that looks like a triangle) ~ Pv ~ R

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Question 1184414: Determine if the given argument is valid or not:
P -> Q
R -> S
~ Qv ~ S
(the 3 dots that looks like a triangle) ~ Pv ~ R
Answer by math_helper(2461) About Me  (Show Source):
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Determine if the given argument is valid or not:
P -> Q
R -> S
~ Qv ~ S
(the 3 dots that looks like a triangle) ~ Pv ~ R
----------- 



Determine if the given argument is valid or not: 



1. P -> Q       Premise

2. R -> S       Premise

3. ~Q v ~S      Premise

//  ∴ ~P v ~R

4.:: ~Q          Conditional Proof (CP) assumption #1

5.:: ~P          4,1 Modus Tollens (MT)

6.:: ~S          CP assumption #2

7.:: ~R          6,2 MT

8.:: ~P v ~R     4-7 Proof by Cases (PBC)

9. ~P v ~R       4-8 CP





The argument is VALID



What the proof shows is this: if not Q (~Q) then we get ~P.  If on the other hand we have ~S, we get ~R, therefore, if either ~Q or ~S then ~P is true or ~R is true (or both).