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This is a question from Discrete Mathematics and Its Applications.

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My focus/question is 1b. What I got was for this question was (English translation)

There is a student in your class who has sent an email message to all other students in the class. After some reflecting, is it necessary to say instead "there is a student in your class who has sent an email message to all students in the class", basically rather than all other, just all? Would this be necessary because it is entirely possible for y to take the same value of x?(student sending email to himself or herself) Or is my initial response acceptable? To me initially, it didn't make sense in English or situation wise for a student to send a message to himself or herself.

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    $\begingroup$ I think the most accurate mathematical interpretation of the question includes the case where a person can send a message to themselves. (And certainly that's possible in real life, even if it's uncommon.) $\endgroup$ Jan 10, 2015 at 7:53
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    $\begingroup$ The second one; the syntax of quantifiers does not preclude that the "object of the domain" satisying the outer $\exists$ can be referenced by the "all the objects in the domain" corersponding to the inner $\forall$. $\endgroup$ Jan 10, 2015 at 7:54
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    $\begingroup$ I used to send emails to myself as a crude form of cloud storage. (Until I realized that I could just save them as drafts instead.) Also, you could send an email to a mailing list that has you as a member. $\endgroup$
    – user856
    Jan 10, 2015 at 8:18
  • $\begingroup$ @Rahul thanks for that mailing list example. That makes sense $\endgroup$ Jan 10, 2015 at 23:17
  • $\begingroup$ @MauroALLEGRANZA No restrictions have been placed. oh ok. that makes sense $\endgroup$ Jan 10, 2015 at 23:25

1 Answer 1

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The question does not explicitly exclude $x$ and $y$ taking on the same value, and since the "domain for both $x$ and $y$ consists of all students in your class" (emphasis mine), you should indeed omit the word "other."

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