1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Removing negations using logical equivalences

  1. Sep 21, 2011 #1
    1. The problem statement, all variables and given/known data
    Remove negations from this: ¬∀x∃y : (P (x, y) --> (∃z : ¬Q(x, y, z))) using logical equivalences.


    2. Relevant equations
    ¬(∃x : P(x)) is equal to ∀x : ¬(P(x))
    P --> Q is equal to ¬P v Q


    3. The attempt at a solution
    ¬∀x∃y : (P (x, y) --> (∃z : ¬Q(x, y, z)))
    ≡ ¬∀x∃y : (¬P (x, y) v (∃z : ¬Q(x, y, z)))
    ≡ ∃x∀y : ¬ (¬P (x, y) v (∃z : ¬Q(x, y, z)))
    ≡ ∃x∀y : (P (x, y) v ¬(¬(∀z : Q(x, y, z))))
    ≡ ∃x∀y : (P (x, y) v (∀z : Q(x, y, z)))

    I'm wondering if I've applied the logic right. I'm not sure if I can just shift the Not like that from line one to two (counting from the equivalency sign). On line two to line three, I'm assuming that (∃z : ¬Q(x, y, z)) would mean something like "There exists a person who doesn't like math", which would equal to ¬(∀z : Q(x, y, z)) or "Not everyone likes math". Then on line four the Not from the very outside cancels the Not in front of that ∀z. Am I doing this right? I feel like I'm missing something.

    Thanks.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: Removing negations using logical equivalences
  1. Equivalent Models (Replies: 0)

  2. Springs Equivalencies (Replies: 0)

Loading...