Quantificational Logic Proofs.. Second opinion please

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jwass52
 
Reply Tue 19 May, 2009 06:29 pm
Here are a couple of Quantificational Logic Proofs. They seemed a little to easy.. (for me) which leads me to believe that I made a mistake. Does this look like i've done them right? Smile

( I could not get the file attached.. so I will type them out.. being new to Foruming is confusing! LOL )

1) (x)(Gx -> Hx)
2) (x)(Hx -> Ix)
3) (x) ~(Ix v Jx) Conclusion (x) ~Gx

|4) Gx
|5) Gb 4 UI
|6) Gb -> Hb 1 UI
|7) Hb 5,6 MP
|8) Hb -> Gb 2 UI
|9) Ib 7,8 MP
|10) ~(Ib v Jb) 3 UI
|11) ~Ib & ~Jb 10 DeM
|12) ~Ib 11 Simp
|13) Ib & ~Ib 9,12 Conj
|14) (x)Ix & (x)~Ix 13 UG
15) ~Gx 4,14 IP



The second problem goes somewhat like this.... ( so I think ) :sarcastic:

1) (x)(Fx & Gx) conclusion (x)Fx & (x)Gx

2) (Fc & Gc) 1 UI
3) Fc 2 Simp
4) (Gc & Fc) 2 Comm
5) Gc 4 Simp
6) (x) Fx 3 UG
7) (x) Gx 5 UG
8) (x)Fx & (x)Gx 6,7 Conj
 
 

 
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