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
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<pre>

Determine if the given argument is valid or not: 

1. P -> Q       Premise
2. R -> S       Premise
3. ~Q v ~S      Premise
//  &#x2234; ~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).