Question 188807
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1. (p v q) -> r
2. r -> (s <--> t)
3. s -> ~t Therefore: ~p v ~t
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4.  r -> [ (s -> t) & (t -> s) ]                      2  Material Equivalence 
5.  ~r v [ (s -> t) & (t -> s) ]                      4  Material Implication
6.  [~r v (s -> t)] & [~r v (t -> s)]                 5  Distribution
7.  [~r v (t -> s)] & [~r v (s -> t)]                 6  Commutation
8.  ~r v (t -> s)                                     7  Simplification
9.  r -> (t -> s)                                     8  Material Implication
10. (r & t) -> s                                      9  Exportation
11. (r & t) -> ~t                                  3,10  Hypothetical Syllogism
12. r -> (t -> ~t)                                   11  Exportation
13. r -> (~t v ~t)                                   12  Material Implication 
14. r -> ~t                                          13  Tautology
15. (p v q) -> ~t                                  1,14  Hypothetical Syllogism
16. ~(p v q) v ~t                                    15  Material Implication
17. (~p & ~q) v ~t                                   16  DeMorgan's Theorem
18. ~t v (~p & ~q)                                   17  Commutation
19. (~t v ~p) & (~t v ~q)                            18  Distribution
20. ~t v ~p                                          19  Simplification
21. ~p v ~t                                          20  Commutation

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