Are These Logic Problems Valid or Invalid? A Scientific Analysis

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In summary: Yes, the computer windows program is pretty cool. I am still working on it, but I think it will be really helpful.
  • #1
Kr1s
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Hi people, I'm trying to solve a logic problem but I'm having some issues with a couple of them. I appreciate if you can help me with it.

1.- (∀x) (∃y) (x=y)
2.- (∃x) P(x)→(∀y)P(y)

Demostrate if valid or invalid each one.

Thank you!
 
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  • #2
(1)
a=a (axiom)
(Ey) a=y (E+)
(Ax) (Ey) x=y (A+)

(2)
definitely invalid. If an apple is rotten, it does not mean all apples are rotten.
 
  • #3
First at all, thank you for your answer. Now, I have a few questions because looks like I use another symbols .

(1)
a=a (axiom) This means the Universal Specification Ax, where x is a, right?
(Ey) a=y (E+) And this is the product of the US.
(Ax) (Ey) x=y (A+) This is the result adding the Universal Generalization.

Hence, this one is valid.

Tell me if that's right please, thank you very much!
 
  • #4
Oh I think you are using a different deduction system. I am using the intro-elim system, which is a little different, and is more popular with philosophers. I am not too familiar with your system, so can't you , sorry.
 
  • #5
Well when I saw your solution I inmediatly thought that you were using an equivalent to quantifier logic. Results are the same though, so It may be the same answer. First one valid and second one invalid. What do you think?
 
  • #6
Intuitively yes :)
I have seen your system before. I think some of these logic for dummy guide teaches this system. I did not really understand it. So I went to read the Schaum series, which teaches the intro-elim system - which i understand. Now I am writing a computer windows program to help me do it on computers
 
  • #7
Oh, ok. That's pretty awesome, the computer windows program. I wish you succes with it. Thank you for trying to help me. ;-)
 

FAQ: Are These Logic Problems Valid or Invalid? A Scientific Analysis

1. What is a logic problem?

A logic problem is a type of puzzle that requires logical reasoning and deduction to solve. It typically involves a set of clues and a given set of rules, and the solver must use logical thinking to determine the correct solution.

2. What are quantifiers in logic problems?

Quantifiers are words that specify the quantity or scope of a statement in a logic problem. The two most commonly used quantifiers are "all" and "some," which respectively mean "every" and "at least one." These quantifiers help to clarify the relationships between different elements in the problem.

3. How do I use quantifiers to solve a logic problem?

To use quantifiers in a logic problem, you must carefully read the clues and determine which elements are being referred to. Then, you can use the quantifiers to infer relationships between these elements and make deductions based on the given rules and information.

4. Can quantifiers be used in both mathematical and verbal logic problems?

Yes, quantifiers can be used in both mathematical and verbal logic problems. In mathematical logic, quantifiers are often represented symbolically using mathematical symbols such as ∀ (for all) and ∃ (there exists). In verbal logic, quantifiers are usually expressed using words such as "all" and "some."

5. Are quantifiers always necessary in solving logic problems?

No, quantifiers are not always necessary in solving logic problems. Some problems may be straightforward enough to solve without using quantifiers, while others may require the use of quantifiers to make deductions and arrive at the correct solution. It ultimately depends on the complexity of the problem and the solver's logical reasoning skills.

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