document.write( "Question 1189673: I am having trouble solving this proof.
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Algebra.Com's Answer #821218 by math_helper(2461) $\"\"$ $\"About$

You can put this solution on YOUR website!


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document.write( "1. ~S ∧ ~R                Premise  
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document.write( "2. ~S                     1, Simplification (SIMP)
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document.write( "3. ~R                     1, SIMP
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document.write( "4. ~R ∧ ~S                3,2 Conjunction Introduction (CI)
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document.write( "// Note, we could have just done Commutation of 1 to arrive at (~R ∧ ~S) in one step
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document.write( "5.:: S v R                Conditional Proof (CP) assumption #1
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document.write( "// Either S or R is true, let's assume S is true first...
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document.write( "6.:: S                    CP assumption #2 
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document.write( "7.:: ~(~R ∧ ~S)           Clearly (~R ∧ ~S) can not be true, because S is true.  The rule name here escapes me.
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document.write( "// Now assume R is true
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document.write( "8.:: R                    CP assumption #3
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document.write( "9.:: ~(~R ∧ ~S)           Clearly (~R ∧ ~S) can not be true, because R is true.  Same rule as line 7.
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document.write( "10.:: (S v R) --> ~(~R ∧ ~S)     5-9, CP
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document.write( "11.:: (~R ∧ ~S) --> ~(S v R)     10, Transposition (if A --> B then ~B --> ~A)
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document.write( "12. (~R ∧ ~S) --> ~(S v R)       5-11, CP
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document.write( "*DONE*
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