SOLUTION: 1). ~(K•L) 2). K -> L Therefore, ~K

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Question 1204425: 1). ~(K•L)
2). K -> L
Therefore, ~K
Found 2 solutions by Edwin McCravy, math_tutor2020:
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!

1).     ~(K•L)
2).      K -> L  Therefore,   ~K

                 | 3).   ~~K   Assumption for Indirect Proof
                 | 4).   K,       3, Double Negation
                 | 5).   L,       2, Modus Ponens
                 | 6).   ~K v ~L  1, DeMorgan's Law
                 | 7).   ~L v ~K  6, Commutation 
                 | 8).   ~~L      5, Double Negation
                 | 9).   ~K     7,8, Disjunctive syllogism 
                 |10).   K•~K   4,9, Conjunction 
11).     ~K           Lines 4-10 Indirect Proof

Edwin
Answer by math_tutor2020(3816)   (Show Source): You can put this solution on YOUR website!

I'll use the ampersand symbol & in place of the center dot.
NumberStatementLine(s) UsedReason
1~(K & L)
2K --> L
:.~K
3~K v ~L1De Morgan’s Law
4K --> ~L3Material Implication
5L --> ~K4Transposition
6K --> ~K2,5Hypothetical Syllogism
7~K v ~K6Material Implication
8~K7Tautology

Refer to these rules of inference and replacement
https://logiccurriculum.com/2019/02/09/rules-for-proofs/
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