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LOGIC DEDUCTIONS

 
 
Reply Sat 27 Apr, 2013 03:09 pm
Please see RULES below
I need help with these...Supply the rule used and the numbers of any earlier lines the rule requires.
1 1. PvQ
2. R&~Q /.: P

2. 1. TvP
2. P-->S /.: ~T-->S

3. 1. Qv~S
2. Q-->P /.: S-->P

4. 1. 1. ~Sv~R
2. P-->(S&R) /.: ~P

5. 1. ~PvS
2. ~T-->~S /.: P-->T

6. 1. F-->R
2. L-->S
3. ~C
4. (R&S)-->C /.: ~Fv~L

7. 1. (S&R)-->P
2. (R-->P)-->W
3. S /.:W

8. 1. ~L-->(~P-->M)
2. ~(PvL) /.: M

EXAMPLE:
1. R-->P
Q-->R /.: Q-->P
ANSWER:
3. Q-->P 1, 2, CHAIN ARGUMENT

Group 1 rules:
1. MODUS PONENS (MP)
P-->Q
P(underlined)
Q

2. MODUS TOLLENS (MT)
P-->Q
~Q (underlined)
~P

3. CHAIN ARGUMENT (CA)
P-->Q
Q-->R (underlined)
P-->R

4. DISJUNCTIVE ARGUMENT (DA)
P v Q P v Q
~P (underlined) ~Q (underlined)
Q P

5. SIMPLICATION (SIM)
P & Q (underlined) P & Q (underlined)
P Q

6. CONJUNCTION (CONJ)
P
Q (underlined)
P & Q

7. ADDITION (ADD)
P (underlined) Q (underlined)
P v Q P v Q

8. CONSTRUCTIVE DILEMMA (CD)
P-->Q
R-->S
P v R (underlined)
Q v S

9. DESTRUCTIVE DILEMMA (DD)
P-->Q
R-->S
~Q v ~S (underlined)
~P v ~R

GROUP 2 RULES
10. DOUBLE NEGATION (DN)
P-->~~P

11. COMMUTATION (COM)
(P&Q)<-->(Q&P)
(PvQ)<-->(QvP)

12. IMPLICATION (IMPL)
(P-->Q)<-->(~PvQ)

13. CONTRAPOSITION (CONTR)
(P-->Q<-->(~Q-->~P)

14, DEMORGAN'S LAW (DEM)
~(P&Q)<-->(~Pv~Q)
~(PvQ)<-->(~P&~Q)

15. EXPORTATION (EXPORT)
[P-->(Q-->R)]<-->[(P&Q)-->R]

16. ASSOCIATION (ASSOC)
[P&(Q&R)]<-->[(P&Q)&R]
[Pv(QvR)]<-->[(PvQ)vR]

17. DISTRIBUTION (DIST)
[P&(QvR)]<-->[(P&Q)v(P&R)]
[Pv(Q&R)]<-->[(PvQ)&(PvR)]

18. TAUTOLOGY (TAUT)
(PvP)<-->P
(P&P)<-->P
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markr
 
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Reply Sat 27 Apr, 2013 07:35 pm
@lisalesa29,
I've shown you lots of examples. Why don't you take a crack at these?
lisalesa29
 
  1  
Reply Mon 29 Apr, 2013 11:49 am
@markr,
I tried...I just don't get it..have two more assign after this and I am done with this class. Thank god! lol. Thanks for all your help!
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