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# Natural Deduction Proof

Posted on 2010-11-14

Hey,

I have question about Natural Deduction Proof.

This is a homework question from logic class. I tried, but kept getting stuck

I could use bunch of rules such as

Quantifier rules, Universal Instantiation rule, Existential Generalization rule, Existential Instantiation rule, Universal Generalization rule.

The problem is,

((¿xP(x) v ¿yQ(y)) --> ¿z(P(z) v Q(z)))

If for all x, P(x) or for all x, Q(x), then for all z, either P(z) or Q(z).

I have to prove this, but its really confusing to me.

I was given an example

1. | \/x/\yF(x,y) pr

2. | /\yF(x2,y) EI 1 x2

3. | F(x2,x1) UI 2

4. | \/xF(x,x1) EG 3

5. | /\y\/xF(x,y) UG 4 x1

6. (\/x/\yF(x,y) --> /\y\/xF(x,y) cd

/\ = ¿

I kind of follow this one, but i can't apply it to other one.

Any kind of help is appreciated.