This is a question from Discrete Mathematics and Its Applications.
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.
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."