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.