HELP! Predicate Logic Proof!?
I need help with this predicate logic proof. I can use existential instantiation, universal generalization, existential generalization, universal instantiation, any of the basic rules of inference, replacement rules, and CP and IP.
Any help would be appreciated!
1. (x)(Fx ⊃ Gx)
2. ~((∃x)Gx v (∃x)Hx)
The conclusion I need to find is : ~(∃x)Fx
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Verified answer
Hi
Do you use dependency numbers or scope lines (or something else entirely)? I'll leave you to put these in as appropriate.
1. (Vx)(Fx > Gx) Premise
2. ~((Ex)(Gx) v (Ex)(Hx)) Premise
I 3. (Ex)(Fx) Assumption
I I 4. Fa Assumption
I I 5. Fa > Ga 1 Universal Instantiation
I I 6. Ga 4,5 Modus Ponens
I I 7. (Ex)(Gx) 6 Existential Generalization
I 8. (Ex)(Gx) 3,4,7 Existential Instantiation
I 9. (Ex)(Gx) v (Ex)(Hx) 8 Addition
10. (Ex)(Fx) > ((Ex)(Gx) v (Ex)(Hx)) 3,9 Conditional Proof
11. ~(Ex)(Fx) 2,10 Modus Tollens
I hope this helps :-)