For the negation of statement

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∃y ∈ Z such that ∀x ∈ Z, R(x + y)
∀x ∈ Z, ∃y ∈ Z such that R(x + y)



Base on this two rule
"For all x, A(x)" negation:"There exist x such that not A(x)"
"There exists x such that A(x)" negation:"For every x, not A(x)"



what I did is "∀y ∈ Z, not ∀x ∈ Z, R(x + y)"
"∃x ∈ Z, ∀y ∈ Z such that R(x + y) "
I wish anyone could help me to check whether this is right or not. Thank you!







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    favorite












    ∃y ∈ Z such that ∀x ∈ Z, R(x + y)
    ∀x ∈ Z, ∃y ∈ Z such that R(x + y)



    Base on this two rule
    "For all x, A(x)" negation:"There exist x such that not A(x)"
    "There exists x such that A(x)" negation:"For every x, not A(x)"



    what I did is "∀y ∈ Z, not ∀x ∈ Z, R(x + y)"
    "∃x ∈ Z, ∀y ∈ Z such that R(x + y) "
    I wish anyone could help me to check whether this is right or not. Thank you!







    share|cite|improve this question






















      up vote
      0
      down vote

      favorite









      up vote
      0
      down vote

      favorite











      ∃y ∈ Z such that ∀x ∈ Z, R(x + y)
      ∀x ∈ Z, ∃y ∈ Z such that R(x + y)



      Base on this two rule
      "For all x, A(x)" negation:"There exist x such that not A(x)"
      "There exists x such that A(x)" negation:"For every x, not A(x)"



      what I did is "∀y ∈ Z, not ∀x ∈ Z, R(x + y)"
      "∃x ∈ Z, ∀y ∈ Z such that R(x + y) "
      I wish anyone could help me to check whether this is right or not. Thank you!







      share|cite|improve this question












      ∃y ∈ Z such that ∀x ∈ Z, R(x + y)
      ∀x ∈ Z, ∃y ∈ Z such that R(x + y)



      Base on this two rule
      "For all x, A(x)" negation:"There exist x such that not A(x)"
      "There exists x such that A(x)" negation:"For every x, not A(x)"



      what I did is "∀y ∈ Z, not ∀x ∈ Z, R(x + y)"
      "∃x ∈ Z, ∀y ∈ Z such that R(x + y) "
      I wish anyone could help me to check whether this is right or not. Thank you!









      share|cite|improve this question











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      asked Aug 19 at 11:55









      TomSophicy

      221




      221




















          2 Answers
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          $forall yin Z text s.t. exists xin Z, text not R(x+y)$



          $exists xin Z, forall yin Z, text s.t. not R(x+y)$






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          • Thank you so much
            – TomSophicy
            Aug 19 at 12:24

















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          The negation of $exists yin Zforall xin Z;P(x,y)$ is:$$forall yin Zexists xin Zneg P(x,y)$$



          Further this is not the same statement as $forall xin Zexists yin Zneg P(x,y)$






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          • Thank you so much
            – TomSophicy
            Aug 19 at 12:24










          Your Answer




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          2 Answers
          2






          active

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          votes








          2 Answers
          2






          active

          oldest

          votes









          active

          oldest

          votes






          active

          oldest

          votes








          up vote
          0
          down vote













          $forall yin Z text s.t. exists xin Z, text not R(x+y)$



          $exists xin Z, forall yin Z, text s.t. not R(x+y)$






          share|cite|improve this answer




















          • Thank you so much
            – TomSophicy
            Aug 19 at 12:24














          up vote
          0
          down vote













          $forall yin Z text s.t. exists xin Z, text not R(x+y)$



          $exists xin Z, forall yin Z, text s.t. not R(x+y)$






          share|cite|improve this answer




















          • Thank you so much
            – TomSophicy
            Aug 19 at 12:24












          up vote
          0
          down vote










          up vote
          0
          down vote









          $forall yin Z text s.t. exists xin Z, text not R(x+y)$



          $exists xin Z, forall yin Z, text s.t. not R(x+y)$






          share|cite|improve this answer












          $forall yin Z text s.t. exists xin Z, text not R(x+y)$



          $exists xin Z, forall yin Z, text s.t. not R(x+y)$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Aug 19 at 11:59









          kevin

          986




          986











          • Thank you so much
            – TomSophicy
            Aug 19 at 12:24
















          • Thank you so much
            – TomSophicy
            Aug 19 at 12:24















          Thank you so much
          – TomSophicy
          Aug 19 at 12:24




          Thank you so much
          – TomSophicy
          Aug 19 at 12:24










          up vote
          0
          down vote













          The negation of $exists yin Zforall xin Z;P(x,y)$ is:$$forall yin Zexists xin Zneg P(x,y)$$



          Further this is not the same statement as $forall xin Zexists yin Zneg P(x,y)$






          share|cite|improve this answer




















          • Thank you so much
            – TomSophicy
            Aug 19 at 12:24














          up vote
          0
          down vote













          The negation of $exists yin Zforall xin Z;P(x,y)$ is:$$forall yin Zexists xin Zneg P(x,y)$$



          Further this is not the same statement as $forall xin Zexists yin Zneg P(x,y)$






          share|cite|improve this answer




















          • Thank you so much
            – TomSophicy
            Aug 19 at 12:24












          up vote
          0
          down vote










          up vote
          0
          down vote









          The negation of $exists yin Zforall xin Z;P(x,y)$ is:$$forall yin Zexists xin Zneg P(x,y)$$



          Further this is not the same statement as $forall xin Zexists yin Zneg P(x,y)$






          share|cite|improve this answer












          The negation of $exists yin Zforall xin Z;P(x,y)$ is:$$forall yin Zexists xin Zneg P(x,y)$$



          Further this is not the same statement as $forall xin Zexists yin Zneg P(x,y)$







          share|cite|improve this answer












          share|cite|improve this answer



          share|cite|improve this answer










          answered Aug 19 at 12:04









          drhab

          87.7k541119




          87.7k541119











          • Thank you so much
            – TomSophicy
            Aug 19 at 12:24
















          • Thank you so much
            – TomSophicy
            Aug 19 at 12:24















          Thank you so much
          – TomSophicy
          Aug 19 at 12:24




          Thank you so much
          – TomSophicy
          Aug 19 at 12:24












           

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