SOLUTION: I am having trouble solving the following propositional logic proofs. 1. Conclusion: N + Y 1. K > (N & P) 2. S > (X & Y) 3. S + K 2. Conclusion: ~Q > ~M 1. M > [ Q + ~(E

Algebra.Com
Question 374237: I am having trouble solving the following propositional logic proofs.
1. Conclusion: N + Y
1. K > (N & P)
2. S > (X & Y)
3. S + K
2. Conclusion: ~Q > ~M
1. M > [ Q + ~(E + H) ]
2. ~E > H
3. Conclusion: A & D
1. ~D > (F & P)
2. ~A > ~(F + P)
3. (F <=> P) > (~~D & A)
4. Conclusion: F > (Y > F)
1. Q
5. Conclusion: ~(~Q > ~X) > ~J
1.J > (M > Q)
2. X > (M + V)
3. J > (V > ~X)
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!
I'll do the first one to get you started. 
1.   K > (N & P)
2.   S > (X & Y)
3.   S + K                             :. N+Y
-------------------------------------------------
4.   [K > (N & P)] & [S > (X & Y)]              1,2 Conjunction
5.   (N & P) + (X & Y)                          4,3 Constructive Dilemma
6.   [(N & P) + X] & [(N & P) + Y]              5   Distibution
7.   [(N & P) + Y] & [(N & P) + X]              6   Commutation
8.   (N & P) + Y                                7   Simplification
9.   Y + (N & P)                                8   Commutation
10.  (Y + N) & (Y + P)                          9   Distribution
11.  Y + N                                      10  Simplification
12.  N + Y                                      11  Commutation


RELATED QUESTIONS

I'm having a ton of trouble figuring out this proof for our take-home quiz. We're only... (answered by jim_thompson5910)
COMPLETE THE FOLLOWING PROOFS USING CONDITIONAL PROOF Premises: 1. Y ⊃ ( N • U) (answered by robertb)
I need help completing proofs for my deductive logic class. Can you help me with this... (answered by jim_thompson5910)
*Proof by induction: Prove that for n >= 1 2^(n+2)>= 2n + 5 I've solved the p(1)... (answered by Edwin McCravy)
1. (P>K) V (F>Y) 2. (PvF) . (KvY) 3. [(P>K)>~N]. [(F>Y)>O] 4. K . ~Y / ~NvO (answered by lynnlo,jim_thompson5910)
Hi, I need help with finishing these proofs for my PHI class I am so confused! :( [1] (answered by Edwin McCravy)
I'm having difficulty solving an exercise. The question is: Prove 3^n >=1+2*n.... (answered by richard1234)
Example: 1. A 2. A>B / B 3. B 1,2 MP ←You add this line 1. G > H 2. ~H /... (answered by ikleyn)
I am working on proofs for my logic homework. Here are the premises: 1. ~S -> (~G v (answered by jim_thompson5910)