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Logic Deductions

 
 
Reply Thu 25 Apr, 2013 10:25 am
PLEASE HELP!
The annotations that explain how each line was derived have been left off the following deductions. For each line, supply the rule used and the numbers of any earlier lines the rule requires.

2. 1. ~P
2. (Q-->R) & (R-->Q)
3. R v P /.: Q
4. R
5. R-->Q
6. Q

3. 1. P-->Q
2. R-->(~S v T)
3. ~P-->R /.: (~Q & S)-->T
4. ~Q-->~P
5. ~Q-->R
6. ~Q-->(~S v T)
7. ~Q-->(S-->T)
8. (-Q&S)-->T

5. 1. ~(S v R)
2. P-->S
3. T-->(P v R) /.: ~T
4. ~S & ~R
5. ~S
6. ~P
7. ~R
8. ~P & ~R
9. ~(P v R)
10. ~T
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markr
 
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Reply Fri 26 Apr, 2013 11:46 pm
@lisalesa29,
2)
1. ~P
2. (Q-->R) & (R-->Q)
3. R v P /.: Q
4. R 1, 3, DA
5. R->Q 2, SIM
6. Q 4, 5, MP

3)
1. P-->Q
2. R-->(~S v T)
3. ~P-->R /.: (~Q & S)-->T
4. ~Q-->~P 1, CONTR
5. ~Q-->R 3, 4, CA
6. ~Q-->(~S v T) 2, 5, CA
7. ~Q-->(S-->T) 6, IMPL
8. (-Q&S)-->T 7, EXP

5.
1. ~(S v R)
2. P-->S
3. T-->(P v R) /.: ~T
4. ~S & ~R 1, DEM
5. ~S 4, SIM
6. ~P 2, 5, MT
7. ~R 4, SIM
8. ~P & ~R 6, 7, CONJ
9. ~(P v R) 8, DEM
10. ~T 3, 9, MT
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