document.write( "Question 1119188: Use conditional proof or indirect proof to establish the truth of the following tautology.\r
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Algebra.Com's Answer #734701 by math_helper(2461) $\"\"$ $\"About$

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document.write( "1.   [~S v ~(~T • ~U)]                          Premise
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document.write( "2.:  [~S v (T v U)]                             Conditional Proof (CP) #1,  1, DeMorgan's (DeM)
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document.write( "3.:  [(~S v T) v U)]                            2, Associative Property (ASSOC)
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document.write( "4.:  [(S —> T) v U)]                            3, Relation of Implication (IMPL)
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document.write( "5.:  [U v (S —> T))]                            4, Commutative Property (COMM)
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document.write( "6.:  [~U —> (S —> T)]                           5, IMPL
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document.write( "7.::  S —> T                                    CP #2, assumption #1
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document.write( "8.::  ~T                                        CP #2, assumption #2
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document.write( "9.::  ~S                                        8,7 Modus Tollens (MT)
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document.write( "10.:: (S —> T)  == (~T —> ~S)                   7-9, CP #2 (shows logical equivalence) 
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document.write( "11.:  [~U —> (~T —> ~S)]                        6,10 logical equivalence 
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document.write( "12. [~S v ~(~T • ~U)] —>  [~U —> (~T —> ~S)]    1-11, CP #1 \n" );
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