Reply Wed 7 Dec, 2016 10:58 am
This is the last one I really need help with

1. (A • B) v (C • D)
2. ~A / C
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Type: Question • Score: 0 • Views: 1,334 • Replies: 9
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Ding an Sich
 
  1  
Reply Wed 7 Dec, 2016 05:55 pm
@agarry13,
What rules are available to you?
agarry13
 
  1  
Reply Wed 7 Dec, 2016 06:45 pm
@Ding an Sich,
All 8 rules of implication and the 10 rules of replacement
0 Replies
 
Kolyo
 
  1  
Reply Wed 7 Dec, 2016 08:17 pm
Spell it out for us. List them.
Ding an Sich
 
  1  
Reply Wed 7 Dec, 2016 08:49 pm
@agarry13,
agarry13 wrote:

This is the last one I really need help with

1. (A • B) v (C • D)
2. ~A / C


I'll give you a hint: take advantage of distribution rules. That's the easiest way to attack this.
0 Replies
 
agarry13
 
  1  
Reply Thu 8 Dec, 2016 11:12 am
@Kolyo,
modus ponens, modus tollens, pure hypothetical syllogism, disjunctive syllogism, constructive dilemma, simplification, conjunction, addition, De Morgan's, commutativity, associativity, distribution, double negation, transpotition, material implication, material equivalence, exportation, and tautology
Kolyo
 
  1  
Reply Thu 8 Dec, 2016 05:11 pm
@agarry13,
I have a hunch Ding an Sich already knew them all.

As for me, I'll try to find a page on the Internet that has those 18 rules written out in symbols.
0 Replies
 
Kolyo
 
  1  
Reply Thu 8 Dec, 2016 08:10 pm
@agarry13,
agarry13 wrote:

modus ponens, modus tollens, pure hypothetical syllogism, disjunctive syllogism, constructive dilemma, simplification, conjunction, addition, De Morgan's, commutativity, associativity, distribution, double negation, transpotition, material implication, material equivalence, exportation, and tautology


http://i.stack.imgur.com/hWRW9.png
0 Replies
 
Kolyo
 
  1  
Reply Thu 8 Dec, 2016 08:21 pm
@agarry13,
Note: I don't really have any formal training in this, but I'm used to proofs, because I was a math major.

agarry13 wrote:

This is the last one I really need help with

1. (A • B) v (C • D)
2. ~A


3. ~A v ~B (addition, from #2)
4. ~(A • B) (DeMorgan, from #3)
5. (C • D) (disjunctive syllogism, with #1 and #4 for premises)
6. C (simplification, from #5)
0 Replies
 
fresco
 
  1  
Reply Fri 9 Dec, 2016 01:30 am
@agarry13,
Exclamation
The proof here is quite simple using the method of 'backward fell swoop'.
Choosing C to be false makes the truth of the disjunction in premise 1. dependent on the truth of both A and B. But premise 2. negates the possible truth of A, therefore C false makes the premises false, hence the argument is valid.
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