SOLUTION: Use conditional proof or indirect proof to establish the truth of the following tautology. [~S v ~(~T • ~U)] ⊃ [~U ⊃ (~T ⊃ ~S)]

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Question 1119188: Use conditional proof or indirect proof to establish the truth of the following tautology.
[~S v ~(~T • ~U)] ⊃ [~U ⊃ (~T ⊃ ~S)]
Answer by math_helper(2461) About Me  (Show Source):
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1.   [~S v ~(~T • ~U)]                          Premise

2.:  [~S v (T v U)]                             Conditional Proof (CP) #1,  1, DeMorgan's (DeM)

3.:  [(~S v T) v U)]                            2, Associative Property (ASSOC)

4.:  [(S —> T) v U)]                            3, Relation of Implication (IMPL)

5.:  [U v (S —> T))]                            4, Commutative Property (COMM)

6.:  [~U —> (S —> T)]                           5, IMPL

7.::  S —> T                                    CP #2, assumption #1

8.::  ~T                                        CP #2, assumption #2

9.::  ~S                                        8,7 Modus Tollens (MT)

10.:: (S —> T)  == (~T —> ~S)                   7-9, CP #2 (shows logical equivalence) 

11.:  [~U —> (~T —> ~S)]                        6,10 logical equivalence 

12. [~S v ~(~T • ~U)] —>  [~U —> (~T —> ~S)]    1-11, CP #1