Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

I Finding useful denial

  1. Jan 14, 2019 #1
    Let U be universe under consideration, and let P(x) and Q(x) be predicate with free variable x. Find a useful denial for (∀x∈U)(P(x)⇒Q(x))

    Then my answer is:

    ¬(∀x∈U)(P(x)⇒Q(x))

    (∃x∈U)¬(P(x)⇒Q(x))

    ¬(P(x)⇒Q(x))

    ¬P∨Q

    I'm unsure if I am on the write path when it comes to finding the useful denial, is this how to do it?

    Thank you.
     
  2. jcsd
  3. Jan 14, 2019 #2

    fresh_42

    User Avatar
    2018 Award

    Staff: Mentor

    Your last step is wrong.
    $$
    \lnot \,(P(x) \Longrightarrow Q(x)) \Longleftrightarrow \exists \,x_0 \in U \, : \,P(x_0) \wedge \lnot \,Q(x_0)
    $$
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?