Nested Quantifiers, “Unique” or “Exactly One” Example












0












$begingroup$


Question



Let L(x, y) be the predicate: "x likes y", where the domains are given by: x is a CS student and y is a kind of food.



Let D(x) be the predicate: "x is a student in this discrete class", where the domain is: all CS students.



Express the following statement using those predicates and any required quantifiers. You may use only universal and existential quantifiers.



(a) There is exactly one CS student who likes tofu.



Response



My answer: ∃x∀y(L(x, tofu) ∧ ((y ≠ x) ⟹ ¬L(x, y))



What is wrong with my answer?






discrete-mathematics logic







share|cite|improve this question









$endgroup$








  • 4




    $begingroup$
    Your answer expresses "there is a CS student who likes tofu and likes no food other than himself." In particular, this student has to be tofu.
    $endgroup$
    – Andreas Blass
    Nov 30 '18 at 18:33










  • $begingroup$
    @AndreasBlass This has to be one of the funniest replies that I've seen on MSE
    $endgroup$
    – Andrei
    Dec 1 '18 at 18:49
















0












$begingroup$


Question



Let L(x, y) be the predicate: "x likes y", where the domains are given by: x is a CS student and y is a kind of food.



Let D(x) be the predicate: "x is a student in this discrete class", where the domain is: all CS students.



Express the following statement using those predicates and any required quantifiers. You may use only universal and existential quantifiers.



(a) There is exactly one CS student who likes tofu.



Response



My answer: ∃x∀y(L(x, tofu) ∧ ((y ≠ x) ⟹ ¬L(x, y))



What is wrong with my answer?






discrete-mathematics logic







share|cite|improve this question









$endgroup$








  • 4




    $begingroup$
    Your answer expresses "there is a CS student who likes tofu and likes no food other than himself." In particular, this student has to be tofu.
    $endgroup$
    – Andreas Blass
    Nov 30 '18 at 18:33










  • $begingroup$
    @AndreasBlass This has to be one of the funniest replies that I've seen on MSE
    $endgroup$
    – Andrei
    Dec 1 '18 at 18:49














0












0








0





$begingroup$


Question



Let L(x, y) be the predicate: "x likes y", where the domains are given by: x is a CS student and y is a kind of food.



Let D(x) be the predicate: "x is a student in this discrete class", where the domain is: all CS students.



Express the following statement using those predicates and any required quantifiers. You may use only universal and existential quantifiers.



(a) There is exactly one CS student who likes tofu.



Response



My answer: ∃x∀y(L(x, tofu) ∧ ((y ≠ x) ⟹ ¬L(x, y))



What is wrong with my answer?






discrete-mathematics logic







share|cite|improve this question









$endgroup$




Question



Let L(x, y) be the predicate: "x likes y", where the domains are given by: x is a CS student and y is a kind of food.



Let D(x) be the predicate: "x is a student in this discrete class", where the domain is: all CS students.



Express the following statement using those predicates and any required quantifiers. You may use only universal and existential quantifiers.



(a) There is exactly one CS student who likes tofu.



Response



My answer: ∃x∀y(L(x, tofu) ∧ ((y ≠ x) ⟹ ¬L(x, y))



What is wrong with my answer?






discrete-mathematics logic




discrete-mathematics logic






share|cite|improve this question













share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Nov 30 '18 at 18:04









Nicholas AdamouNicholas Adamou

32




32








  • 4




    $begingroup$
    Your answer expresses "there is a CS student who likes tofu and likes no food other than himself." In particular, this student has to be tofu.
    $endgroup$
    – Andreas Blass
    Nov 30 '18 at 18:33










  • $begingroup$
    @AndreasBlass This has to be one of the funniest replies that I've seen on MSE
    $endgroup$
    – Andrei
    Dec 1 '18 at 18:49














  • 4




    $begingroup$
    Your answer expresses "there is a CS student who likes tofu and likes no food other than himself." In particular, this student has to be tofu.
    $endgroup$
    – Andreas Blass
    Nov 30 '18 at 18:33










  • $begingroup$
    @AndreasBlass This has to be one of the funniest replies that I've seen on MSE
    $endgroup$
    – Andrei
    Dec 1 '18 at 18:49








4




4




$begingroup$
Your answer expresses "there is a CS student who likes tofu and likes no food other than himself." In particular, this student has to be tofu.
$endgroup$
– Andreas Blass
Nov 30 '18 at 18:33




$begingroup$
Your answer expresses "there is a CS student who likes tofu and likes no food other than himself." In particular, this student has to be tofu.
$endgroup$
– Andreas Blass
Nov 30 '18 at 18:33












$begingroup$
@AndreasBlass This has to be one of the funniest replies that I've seen on MSE
$endgroup$
– Andrei
Dec 1 '18 at 18:49




$begingroup$
@AndreasBlass This has to be one of the funniest replies that I've seen on MSE
$endgroup$
– Andrei
Dec 1 '18 at 18:49










2 Answers
2






active

oldest

votes


















1












$begingroup$

Let $t$ stand for tofu. Let $CS$ be the set of all CS majors.



Then
begin{align}
&
&
&exists! x in CS , L(x,t)
&
&text{Exactly one CS student likes $t$.}
\[1ex]
&text{i.e.,} &quad
&exists x in CS , bigl[ L(x,t) wedge forall y in CS , (L(y,t) to y = x ) bigr]
&
&begin{array}
$text{A CS student $x$ likes $t$, and every} \ text{CS student that likes $t$ must be $x$.}end{array}
end{align}






share|cite|improve this answer









$endgroup$





















    0












    $begingroup$

    There is at least one student $x$ that likes tofu such as all students in the CS class that are not $x$ don't like tofu. It's easy to show that $x$ is unique.






    share|cite|improve this answer









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      2 Answers
      2






      active

      oldest

      votes








      2 Answers
      2






      active

      oldest

      votes









      active

      oldest

      votes






      active

      oldest

      votes









      1












      $begingroup$

      Let $t$ stand for tofu. Let $CS$ be the set of all CS majors.



      Then
      begin{align}
      &
      &
      &exists! x in CS , L(x,t)
      &
      &text{Exactly one CS student likes $t$.}
      \[1ex]
      &text{i.e.,} &quad
      &exists x in CS , bigl[ L(x,t) wedge forall y in CS , (L(y,t) to y = x ) bigr]
      &
      &begin{array}
      $text{A CS student $x$ likes $t$, and every} \ text{CS student that likes $t$ must be $x$.}end{array}
      end{align}






      share|cite|improve this answer









      $endgroup$


















        1












        $begingroup$

        Let $t$ stand for tofu. Let $CS$ be the set of all CS majors.



        Then
        begin{align}
        &
        &
        &exists! x in CS , L(x,t)
        &
        &text{Exactly one CS student likes $t$.}
        \[1ex]
        &text{i.e.,} &quad
        &exists x in CS , bigl[ L(x,t) wedge forall y in CS , (L(y,t) to y = x ) bigr]
        &
        &begin{array}
        $text{A CS student $x$ likes $t$, and every} \ text{CS student that likes $t$ must be $x$.}end{array}
        end{align}






        share|cite|improve this answer









        $endgroup$
















          1












          1








          1





          $begingroup$

          Let $t$ stand for tofu. Let $CS$ be the set of all CS majors.



          Then
          begin{align}
          &
          &
          &exists! x in CS , L(x,t)
          &
          &text{Exactly one CS student likes $t$.}
          \[1ex]
          &text{i.e.,} &quad
          &exists x in CS , bigl[ L(x,t) wedge forall y in CS , (L(y,t) to y = x ) bigr]
          &
          &begin{array}
          $text{A CS student $x$ likes $t$, and every} \ text{CS student that likes $t$ must be $x$.}end{array}
          end{align}






          share|cite|improve this answer









          $endgroup$



          Let $t$ stand for tofu. Let $CS$ be the set of all CS majors.



          Then
          begin{align}
          &
          &
          &exists! x in CS , L(x,t)
          &
          &text{Exactly one CS student likes $t$.}
          \[1ex]
          &text{i.e.,} &quad
          &exists x in CS , bigl[ L(x,t) wedge forall y in CS , (L(y,t) to y = x ) bigr]
          &
          &begin{array}
          $text{A CS student $x$ likes $t$, and every} \ text{CS student that likes $t$ must be $x$.}end{array}
          end{align}







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Nov 30 '18 at 18:28









          Mark TwainMark Twain

          1,861510




          1,861510























              0












              $begingroup$

              There is at least one student $x$ that likes tofu such as all students in the CS class that are not $x$ don't like tofu. It's easy to show that $x$ is unique.






              share|cite|improve this answer









              $endgroup$


















                0












                $begingroup$

                There is at least one student $x$ that likes tofu such as all students in the CS class that are not $x$ don't like tofu. It's easy to show that $x$ is unique.






                share|cite|improve this answer









                $endgroup$
















                  0












                  0








                  0





                  $begingroup$

                  There is at least one student $x$ that likes tofu such as all students in the CS class that are not $x$ don't like tofu. It's easy to show that $x$ is unique.






                  share|cite|improve this answer









                  $endgroup$



                  There is at least one student $x$ that likes tofu such as all students in the CS class that are not $x$ don't like tofu. It's easy to show that $x$ is unique.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered Nov 30 '18 at 18:13









                  AndreiAndrei

                  11.6k21026




                  11.6k21026






























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