Question 531393: hey can you help me with these proofs?
1. ~(J & K) prem
2. ~(L & M) prem
3. J v L / ~(K & M) prem/conc
4.
5.
6.
7.
8.
1.~ P v Q prem
2.~ R > ~Q prem
3.~(R & ~S) / P > S prem / conc
4.
5.
6.
7.
8.
Found 2 solutions by solver91311, jim_thompson5910:
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website!
You'll have to come up with the reasons but it should go something like this:
~(J & K) -> ~J v ~K
~(L & M) -> ~L v ~M
Since J v L, ~(~J & ~L)
~(~J & ~L) -> ~K v ~M -> ~(K & M)
That last step, in English: Since J and L cannot both be false, one or the other or both of K and M must be false, so both K and M cannot be true.
John
My calculator said it, I believe it, that settles it
Answer by jim_thompson5910(35256)  (Show Source):
You can put this solution on YOUR website!
1. ~(J & K) prem
2. ~(L & M) prem
3. J v L / ~(K & M) prem/conc
4. ~J v ~K 1 DM
5. ~L v ~M 2 DM
6. J -> ~K 4 MI
7. L -> ~M 5 MI
8. (J -> ~K) & (L -> ~M) 6,7 Conj
9. ~K v ~M 8,3 CD
10. ~(K & M) 9 DM
Abbreviations/Acronyms Used:
CD = Constructive Dilemma
Conj = Conjunction
MI = Material Implication
DM = De Morgan's Law
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1. ~P v Q prem
2. ~R > ~Q prem
3. ~(R & ~S) / P > S prem / conc
4. ~~Q > ~~R 2 Trans
5. Q > R 4 DN
6. P > Q 1 MI
7. P > R 6,5 HS
8. ~R v ~~S 3 DM
9. ~R v S 8 DN
10. ~~R > S 9 MI
11. R > S 10 DN
12. P > S 7,11 HS
Abbreviations/Acronyms Used:
Trans = Transposition
DN = Double Negation
MI = Material Implication
HS = Hypothetical Syllogism
DM = De Morgan's Law
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