The following sentence needs to be translated from english to a proposition using universal and existential quantifiers.

Everyone in this class knows exactly one person that goes to university.

I have been using the following predicates:

let U = all people

let C(x) = x in this class

let K(x,y) = x knows y

let N (y) = y goes to university

My attempt:

∀x (C(x) ∧ N (y) ∧ K(x,y)


I am struggling to denote the exactly one portion and keeping the integrity of the sentence.

  • 1
    $\begingroup$ Interpret the sentence in the following way: If $x$ is in this class then $x$ knows $y$ and if $x$ also knows $z$ then $y=z$. $\endgroup$
    – user170039
    Feb 4, 2018 at 3:41
  • $\begingroup$ And don't forget to existentially quantify $y$: for every $x$ in the class there exists a $y$ who goes to university. $\endgroup$ Feb 4, 2018 at 4:27


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