Sixth grade math (number related) problem

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$begingroup$


We have this statement (about rational numbers, btw):



If $m-n+p = p$ and $ m neq n neq 0$ then $ m = -n$



Is this true?

a) always

b) never

c) sometimes



The given answer is b) but:

1) this textbook often has some wrong answers and

2) this question got me really thinking...



According to the truth table of the implication if the premise is false, then the whole implication is true, no matter what the conclusion is.
In this case the premise is a conjunction of several facts, two of which are contradictory ($m = n $ and $m neq n$).
So the premise is false. And so I conclude the whole implication is true.

Then... what does that mean? I guess it means the correct answer is a).










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    2












    $begingroup$


    We have this statement (about rational numbers, btw):



    If $m-n+p = p$ and $ m neq n neq 0$ then $ m = -n$



    Is this true?

    a) always

    b) never

    c) sometimes



    The given answer is b) but:

    1) this textbook often has some wrong answers and

    2) this question got me really thinking...



    According to the truth table of the implication if the premise is false, then the whole implication is true, no matter what the conclusion is.
    In this case the premise is a conjunction of several facts, two of which are contradictory ($m = n $ and $m neq n$).
    So the premise is false. And so I conclude the whole implication is true.

    Then... what does that mean? I guess it means the correct answer is a).










    share|cite|improve this question









    $endgroup$














      2












      2








      2





      $begingroup$


      We have this statement (about rational numbers, btw):



      If $m-n+p = p$ and $ m neq n neq 0$ then $ m = -n$



      Is this true?

      a) always

      b) never

      c) sometimes



      The given answer is b) but:

      1) this textbook often has some wrong answers and

      2) this question got me really thinking...



      According to the truth table of the implication if the premise is false, then the whole implication is true, no matter what the conclusion is.
      In this case the premise is a conjunction of several facts, two of which are contradictory ($m = n $ and $m neq n$).
      So the premise is false. And so I conclude the whole implication is true.

      Then... what does that mean? I guess it means the correct answer is a).










      share|cite|improve this question









      $endgroup$




      We have this statement (about rational numbers, btw):



      If $m-n+p = p$ and $ m neq n neq 0$ then $ m = -n$



      Is this true?

      a) always

      b) never

      c) sometimes



      The given answer is b) but:

      1) this textbook often has some wrong answers and

      2) this question got me really thinking...



      According to the truth table of the implication if the premise is false, then the whole implication is true, no matter what the conclusion is.
      In this case the premise is a conjunction of several facts, two of which are contradictory ($m = n $ and $m neq n$).
      So the premise is false. And so I conclude the whole implication is true.

      Then... what does that mean? I guess it means the correct answer is a).







      logic education rational-numbers






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      asked Jan 19 at 22:18









      peter.petrovpeter.petrov

      5,439821




      5,439821




















          1 Answer
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          $begingroup$

          I believe this is a poorly worded math problem, sixth grade or otherwise. The statement



          $$m neq n neq 0$$



          is possibly meant to be something like



          $$m, n neq 0$$



          instead. This would be to ensure that $m = n$ and $m = -n$ can't both be true simultaneously as it only occurs when $m = n = 0$.



          This is only a guess, but it would mean the question would then be consistent with the textbook's provided answer.






          share|cite|improve this answer











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            1 Answer
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            active

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            1 Answer
            1






            active

            oldest

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            active

            oldest

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            active

            oldest

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            6












            $begingroup$

            I believe this is a poorly worded math problem, sixth grade or otherwise. The statement



            $$m neq n neq 0$$



            is possibly meant to be something like



            $$m, n neq 0$$



            instead. This would be to ensure that $m = n$ and $m = -n$ can't both be true simultaneously as it only occurs when $m = n = 0$.



            This is only a guess, but it would mean the question would then be consistent with the textbook's provided answer.






            share|cite|improve this answer











            $endgroup$

















              6












              $begingroup$

              I believe this is a poorly worded math problem, sixth grade or otherwise. The statement



              $$m neq n neq 0$$



              is possibly meant to be something like



              $$m, n neq 0$$



              instead. This would be to ensure that $m = n$ and $m = -n$ can't both be true simultaneously as it only occurs when $m = n = 0$.



              This is only a guess, but it would mean the question would then be consistent with the textbook's provided answer.






              share|cite|improve this answer











              $endgroup$















                6












                6








                6





                $begingroup$

                I believe this is a poorly worded math problem, sixth grade or otherwise. The statement



                $$m neq n neq 0$$



                is possibly meant to be something like



                $$m, n neq 0$$



                instead. This would be to ensure that $m = n$ and $m = -n$ can't both be true simultaneously as it only occurs when $m = n = 0$.



                This is only a guess, but it would mean the question would then be consistent with the textbook's provided answer.






                share|cite|improve this answer











                $endgroup$



                I believe this is a poorly worded math problem, sixth grade or otherwise. The statement



                $$m neq n neq 0$$



                is possibly meant to be something like



                $$m, n neq 0$$



                instead. This would be to ensure that $m = n$ and $m = -n$ can't both be true simultaneously as it only occurs when $m = n = 0$.



                This is only a guess, but it would mean the question would then be consistent with the textbook's provided answer.







                share|cite|improve this answer














                share|cite|improve this answer



                share|cite|improve this answer








                edited Jan 19 at 22:45

























                answered Jan 19 at 22:24









                John OmielanJohn Omielan

                2,331212




                2,331212



























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