document.write( "Question 1188424: Formal proof: In the text box below, use the proof method (M9) to construct a formal proof to demonstrate that the following argument is valid: \r
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Algebra.Com's Answer #820094 by math_helper(2461) $\"\"$ $\"About$

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document.write( "1.  (H v K) ⊃ (L v K)    Premise
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document.write( "2.  M ⊃ [H⊃ (N • ~L)]    Premise   
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document.write( "// Show  (M • H) ⊃ (N • K)
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document.write( "3.:: M • H               Conditional Proof (CP) assumption #1
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document.write( "4.:: M                   3, Simplification (SIMP)
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document.write( "5.:: H⊃ (N • ~L)         4,2  Modus Ponens (MP)
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document.write( "6.:: H                   3, SIMP
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document.write( "7.:: N • ~L              6,5 MP
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document.write( "8.:: N                   7, SIMP
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document.write( "9.:: ~(H v K) v (L v K)    1, Material Implication (MI)
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document.write( "10.:: (~H • ~K) v (L v K)  10, DeMorgan's (DM)  
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document.write( "11.:: ~L                 7, SIMP
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document.write( "12.:: H v K              6, Addition (ADD)
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document.write( "13.:: L v K              12,1  MP
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document.write( "14.:: K                  11,13 Disjunctive Syllogism (DS)
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document.write( "15.:: N • K              8,14 Conjunction (CONJ)
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document.write( "16. (M • H) ⊃ (N • K)    3-15, CP
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