Still celebrating National IT Professionals Day with 3 months of free Premium Membership. Use Code ITDAY17

x
Solved

# Natural Deduction Proof

Posted on 2010-11-14
Medium Priority
924 Views
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.

0
Question by:errang
[X]
###### Welcome to Experts Exchange

Add your voice to the tech community where 5M+ people just like you are talking about what matters.

• Help others & share knowledge
• Earn cash & points

LVL 12

Accepted Solution

larsrohr earned 2000 total points
ID: 34133251
Since this is homework, we wouldn't want to give too much away.  :-)

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?
0

Author Closing Comment

ID: 34166793
Thanks, found the solution.
0

## Featured Post

Question has a verified solution.

If you are experiencing a similar issue, please ask a related question

Before You Read The Article Please make sure you understand these two concepts: Variable Scope (http://www.php.net/manual/en/language.variables.scope.php) and Property Visibility (http://www.php.net/manual/en/language.oop5.visibility.php).  And to …
Introduction This article discusses the Chain of Responsibility pattern, explaining What it is;Why it is; andHow it is At the end of this article, I hope you will be able to describe the use and benefits of Chain of Responsibility.  Backgrou…
This is a video describing the growing solar energy use in Utah. This is a topic that greatly interests me and so I decided to produce a video about it.
Finds all prime numbers in a range requested and places them in a public primes() array. I've demostrated a template size of 30 (2 * 3 * 5) but larger templates can be built such 210  (2 * 3 * 5 * 7) or 2310  (2 * 3 * 5 * 7 * 11). The larger templa…
###### Suggested Courses
Course of the Month10 days, 1 hour left to enroll