Question 188876: I am stuck, I do not know how to finish this.
1. (LvM).(Lv~S)
2. A->~L
3. A->(~MvS) :. ~A
|4. ~A assume
||5. ~MvS assume
||6. LvM 1, simp
||7. Lv~S 1, simp
||8. ~~(A->~L) 2, DN
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! Here's one way to do it:
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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