Question 188876
Here's one way to do it:


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1. (L v M) & (L v ~S)
2. A -> ~L
3. A -> (~M v S)  :.  ~A
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4.  L v (M & ~S)              1    Distribution
5.  ~~L v (M & ~S)            4    Double Negation
6.  ~L -> (M & ~S)            5    Material Implication
7.  A -> (M & ~S)           2,6    Hypothetical Syllogism
8.  A -> (~M v ~~S)           3    Double Negation
9.  A -> ~(M & ~S)            8    De Morgan's Law
10. ~~(M & ~S) -> ~A          9    Transposition
11. (M & ~S) -> ~A           10    Double Negation
12. A -> ~A                7,11    Hypothetical Syllogism
13. ~A v ~A                  12    Material Implication
14. ~A                       13    Tautology
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