1. Limited time only! Sign up for a free 30min personal 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!

Quantified Propositions

  1. Feb 18, 2015 #1
    1. The problem statement, all variables and given/known data

    I've been trying to translate the following sentences into quantified propositions by making sure I state all propositional functions that I use and any assumptions that I make.

    Can you see if I'm on the right track here?

    2. Relevant equations


    3. The attempt at a solution

    1. All engineers are good with computers.

    Let ##E(x)## be '##x## is an engineer' and ##C(x)## be '##x## is good with computers,'
    where the domain of ##x## is all people in the world.

    Then, ##\forall x\ E(x) \rightarrow C(x)##.


    2. Some mathematicians also like poetry.

    Let ##M(x)## be '##x## is a mathematician' and ##P(x)## be '##x## also likes poetry,'
    where the domain of ##x## is all people in the world.

    Then, ##\exists x\ M(x) \land P(x)##.

    3. There are no writers who do not like reading books.

    Let ##W(x)## be '##x## is a writer' and ##B(x)## be '##x## likes reading books,'
    where the domain of '##x## is all people in the world.

    Then, ##\neg\ \exists x\ W(x) \land \neg B(x)##.

    4. Not every athlete is famous.

    Let ##A(x)## be '##x## is an athlete' and ##F(x)## be '##x## is famous,'
    where the domain of ##x## is all people in the world.

    Then, ##\neg \forall x\ A(x) \rightarrow F(x)##.

    5. Only scientists properly value civilisation.

    Let ##S(x)## be '##x## is a scientist' and ##C(x)## be '##x## properly values civilisation,'
    where the domain of ##x## is all people in the world.

    Then, ##\forall x\ C(x) \rightarrow S(x)##.
     
  2. jcsd
  3. Feb 19, 2015 #2

    Stephen Tashi

    User Avatar
    Science Advisor

    You are on the right track. Is your course material particular about using parentheses and brackets?

    For example,

    ##\neg \forall x\ A(x) \rightarrow F(x)##.

    could be written as:

    ##\neg (\forall x (\ A(x) \rightarrow F(x)) )##
     
  4. Feb 26, 2015 #3
    No it's not very picky about the parenthesis.

    Thanks, though!
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Quantified Propositions
  1. Propositional Logic (Replies: 9)

  2. Compound Propositions (Replies: 2)

Loading...