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Logic Problem, quantifiers

  1. Jul 1, 2012 #1
    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!!!
     
  2. jcsd
  3. Jul 3, 2012 #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.
     
  4. Jul 3, 2012 #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!
     
  5. Jul 3, 2012 #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.
     
  6. Jul 3, 2012 #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?
     
  7. Jul 3, 2012 #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
     
  8. Jul 3, 2012 #7
    Oh, ok. That's pretty awesome, the computer windows program. I wish you succes with it. Thank you for trying to help me. ;-)
     
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