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1. K > ~K
2. (~S v U)> K
/ S
-------------------------------------------------------
3. ~~K > ~K 1 DN
4. ~K v ~K 3 MI
5. ~K 4 Taut
6. ~(~S v U) 2,5 MT
7. ~~S & ~U 6 DM
8. S & ~U 7 DN
9. S 8 Simp
Abbreviations/Acronyms Used:
DN = Double Negation
MI = Material Implication
Taut = Tautology
MT = Modus Tollens
DM = De Morgan's Law
Simp = Simplification