Results 1 to 3 of 3

Thread: Could anyone help me with this problem on the interpretation of first-order logic?

  1. #1
    Newbie
    Joined
    Mar 2015
    From
    United Kingdom
    Posts
    3

    Could anyone help me with this problem on the interpretation of first-order logic?

    I am a student of logic who just became familiar with first-order predicate logic. I got stuck in this problem. Although I was hinted to translate→into ,∨ to solve the problem, I still have no idea what to do next. Here is the problem:
    Use semantics under the substitution to check whether 1> ∃x (Pa→Qx) ⇔Pa →∃x(Qx)
    2> ∃x (Px→Qa) ⇔∃x(Px) →Qa. If either 1> or 2> fails, can you suggest a rectification?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    20,491
    Thanks
    2329
    Awards
    1

    Re: Could anyone help me with this problem on the interpretation of first-order logic

    Quote Originally Posted by yytsau View Post
    I am a student of logic who just became familiar with first-order predicate logic. I got stuck in this problem. Although I was hinted to translate→into ,∨ to solve the problem, I still have no idea what to do next. Here is the problem:
    Use semantics under the substitution to check whether 1> ∃x (Pa→Qx) ⇔Pa →∃x(Qx)
    2> ∃x (Px→Qa) ⇔∃x(Px) →Qa. If either 1> or 2> fails, can you suggest a rectification?
    Please use grouping symbols.
    $\begin{array}{l}
    \left( {\exists x} \right)\left[ {P(a) \to Q(x)} \right]\\
    \left( {\exists x} \right)\left[ {\neg P(a) \vee Q(x)} \right]\\
    \neg P(a) \vee \left( {\exists x} \right)\left[ {Q(x)} \right]\\
    \left( {P(a) \to \left( {\exists x} \right)\left[ {Q(x)} \right]} \right)
    \end{array}$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2015
    From
    United Kingdom
    Posts
    3

    Re: Could anyone help me with this problem on the interpretation of first-order logic

    Thanks for your response. But I don't think it is the format that needs a rectification.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. First order logic! need help
    Posted in the Discrete Math Forum
    Replies: 4
    Last Post: Jan 24th 2013, 05:14 AM
  2. First order logic
    Posted in the Discrete Math Forum
    Replies: 3
    Last Post: Nov 16th 2011, 09:41 AM
  3. First order logic
    Posted in the Discrete Math Forum
    Replies: 5
    Last Post: Feb 10th 2011, 08:10 AM
  4. First order Logic
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: Jan 16th 2011, 05:41 AM
  5. First Order Logic problem with conditionals
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: Jun 10th 2010, 02:10 PM

Search Tags


/mathhelpforum @mathhelpforum