document.write( "Question 1184414: Determine if the given argument is valid or not: \r
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Algebra.Com's Answer #814988 by math_helper(2461) $\"\"$ $\"About$

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Determine if the given argument is valid or not: \r
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document.write( "Determine if the given argument is valid or not: \r
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document.write( "1. P -> Q       Premise
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document.write( "2. R -> S       Premise
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document.write( "3. ~Q v ~S      Premise
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document.write( "//  ∴ ~P v ~R
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document.write( "4.:: ~Q          Conditional Proof (CP) assumption #1
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document.write( "5.:: ~P          4,1 Modus Tollens (MT)
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document.write( "6.:: ~S          CP assumption #2
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document.write( "7.:: ~R          6,2 MT
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document.write( "8.:: ~P v ~R     4-7 Proof by Cases (PBC)
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document.write( "9. ~P v ~R       4-8 CP\r
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document.write( "The argument is VALID\r
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document.write( "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).\r
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