SOLUTION: I am stuck, I do not know how to finish this. 1. (LvM).(Lv~S) 2. A->~L 3. A->(~MvS) :. ~A |4. ~A

Algebra ->  Proofs -> SOLUTION: I am stuck, I do not know how to finish this. 1. (LvM).(Lv~S) 2. A->~L 3. A->(~MvS) :. ~A |4. ~A       Log On


   

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) About Me  (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
-------------------------
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