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New Logic Proofs = New Headache!

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mrmicr
 
Reply Mon 30 Nov, 2009 11:08 pm
i assumed i was on the right track with the logical proofs i was doing but these have officially stomped me. user: emil helped me with the others\ ones by sending her book but somehow the new ones i have received simply aren't making sense. any help with these proofs would be appreciated. perhaps a step or two to get me going.

thanks in advance! i've already learned so much within this community just from reading past threads.


question 1
(S & K) ⊃ R
K
____________
|- S ⊃ R

question 2
G /// (three tier equal symbol) M
G v M
G ⊃ (M ⊃ T)
_________________
|- T

question 3
C ⊃ (~L ⊃ Q)
L ⊃ ~C
~Q
_____________
|- ~C

question 4
K ⊃ (B ⊃ ~M)
D ⊃ (K & M)
_____________
|- D ⊃ ~B
 
Emil
 
Reply Tue 1 Dec, 2009 07:55 am
@mrmicr,
Perhaps if you used the symbols I'm familiar with, then I could help you. I don't know what is meant, for instance, with "⊃". I'm guessing material conditional. And what is "three tier equal symbol"? This "≡" perhaps? What does it mean? Material biconditional maybe. Maybe a definitional material biconditional. Maybe logical equivalence.

Different teachers use different symbols. Sometimes they use the same symbols to mean different things.

P.S. "Emil" is a male name. (A danish one.)
 
mrmicr
 
Reply Tue 1 Dec, 2009 08:09 am
@mrmicr,
firstly, i do apologize for referring to you as a female - i realized your gender once i visited your page. :-).

"⊃" is conditional "only false when antecedent is true and its consequent is false" (if then"

"≡" is biconditional "always having the same truth value" - this is the one i don't quite understand which is another reason i'm having trouble. perhaps both have to either be true or both be false?

hellllllllllllllllp emil!
 
Emil
 
Reply Tue 1 Dec, 2009 09:38 am
@mrmicr,
mrmicr;107266 wrote:
firstly, i do apologize for referring to you as a female - i realized your gender once i visited your page. :-).

"⊃" is conditional "only false when antecedent is true and its consequent is false" (if then"


Careful with saying that material conditionals are "if, then"-statements. There is a large controversy about that.

Quote:
"≡" is biconditional "always having the same truth value" - this is the one i don't quite understand which is another reason i'm having trouble. perhaps both have to either be true or both be false?

hellllllllllllllllp emil!


Biconditionals are just conditionals both ways.

P↔Q =df (P→Q)∧(Q→P)

And yes, the variables need to have the same truth value for the biconditionals to be true. Fill a truth table and see for yourself.
 
 

 
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