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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.

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.

2 Comments

How would you go about starting this proof? (First step or two)

Have you convinced yourself that the statement is true? If so, can you briefly explain in words why it should be true? This often helps in figuring out how your proof should go.

Do you have a Disjunction Elimination rule?

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