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[ARCHIVED THREAD] - For the logic gurus...

Posted: 9/20/2007 8:42:00 PM EDT

Okay, we have a problem for our logic class, and it is stumping the shit out of me. The question goes as follows:

There is a connective X, and three sentence letters p,q, and r. The sentences are formed thus: X(p,q,r). You can combine the X mutiple times, ex. X(p,q,X(p,q,r)). The truth table for this connective is as follows:

p q r X(p,q,r)
T T T F
T T F T
T F T F
T F F T
F T T F
F T F F
F F T T
F F F T

Give a sentence using no connectives other than X which is a logical truth (the sentence can contain no other connectives and will use only the sentence letters p, q, and r. You may use the connective X as many times as you want.)

Anyone have any ideas?

Posted: 9/20/2007 8:54:34 PM EDT

[#1]

X( X(p,(X(p,p,p),p), X(p,X(p,p,p),p), X(p,X(p,p,p),p))

check that. i would take credit, but given to me by a logic phd at berkely :-p.

I took two logic classes, both of which are not sufficient for me to have drunk a fifth of scotch and answer that.

Posted: 9/20/2007 8:57:22 PM EDT

[#2]

PS: favor for a favor, he wants you to do his hw:

show that x=y -> x=z -> x=x -> y=z is a theorem of T (a theory with no nonlogical symbols or axioms) not provable without equality axioms

Posted: 9/20/2007 9:06:23 PM EDT

[#3]

Hey, that absolutely works! Thanks alot, i never thought to just use P, that only means you are dealing with two instances, when its always true or always false. Great stuff. Your friend is very good. Thanks again.

ETA: If he wants me to do that for him, i will happily do so. It wont be the right answer, but i will do it!

Posted: 9/20/2007 9:07:17 PM EDT

[#4]

no problem, brotha. we gots to stick together right? good luck and if you got any more questions shoot me a pm or something.

[ARCHIVED THREAD] - For the logic gurus...

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[ARCHIVED THREAD] - For the logic gurus...

[ARCHIVED THREAD] - For the logic gurus...