document.write( "Question 1149388: Construct deductions for each of the following arguments using Group I rules. (1)
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\n" ); document.write( "1. P → S
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\n" ); document.write( "1. P → S\r
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Algebra.Com's Answer #770721 by math_helper(2461) $\"\"$ $\"About$

You can put this solution on YOUR website!


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document.write( "Needing help with line 4 is the entire problem :-)  If this helps, take time to send 'thanks'... it is much appreciated:\r
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document.write( "1. P --> S     Premise
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document.write( "2. P v Q       Premise
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document.write( "3. Q --> R     Premise
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document.write( "// Show S v R\r
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document.write( "4. ~P v S      1, Material Implication (MI)
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document.write( "5. S v Q       2,4 Resolution (RES)
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document.write( "6. ~Q v R      3, MI
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document.write( "7. R v S       5,6 RES   
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document.write( "*** DONE ***\r
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document.write( "----\r
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document.write( "Alt Proof:
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document.write( "4. R v S       1,2,3 Constructive Dilemma (CD)
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document.write( "*** DONE ***\r
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document.write( "----\r
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document.write( "Alt Proof #2 (Conditional proof):
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document.write( "4.::  ~P       Conditional proof (CP) assumption #1
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document.write( "5.::   Q       4,2 (RES)
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document.write( "6.::   R       5,3 Modus Ponens (MP)  // we've shown R true if P false
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document.write( "7.::   P       CP assumption #2
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document.write( "8.::   S       7,1 MP    // we've shown S true if P true
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document.write( "9.::   S v R   4-8  Proof by Cases (PBC)
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document.write( "10. S v R      4-9 CP
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document.write( "*** DONE ***\r
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document.write( "In CPs, you are applying hypotheticals/scenarios and seeing what logically 
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document.write( "follows; any interesting/useful conclusions can be extracted but the states of the variables do not change (for instance, one can NOT say R is true from line 6::, because that only followed from the ~P assumption on line 4::).  I like to think of CPs as a way to see how the logic flows, without permenantly changing anything.  \r
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