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Translating English Sentences into Logical Expressions with Nested Quanitifiers

  1. Oct 24, 2012 #1
    Hello everyone,

    An example from a homework assignment has me stymied. There are two parts. Here they are:

    First part:
    Let M(x,y) be "x has sent y an e-mail message" and T(x,y) be "x has telephoned y," where the domain consists of all students in your class. Use quantifiers to express each of these statements. (Assume that all e-mail messages that were sent are received, which is not the way things often work.)

    And the statement I'm having problems with:
    There is a student in your class who has not received an e-mail message from anyone else in the class and who has not been called by any other student in the class.

    Here is the answer from the book:
    ∃x∀y(x≠y → (¬M(x,y) ∧ ¬T(y,x)))

    I agree with everything except for the order of x and y after M.
    Why isn't it like this:
    ∃x∀y(x≠y → (¬M(y,x) ∧ ¬T(y,x)))

    After all, since
    M(x,y) = x has sent y an email message
    and T(x,y) = x has telephoned y
    it seems that y should come before x in both instances in the answer.

    Could someone please clarify this for me.
  2. jcsd
  3. Oct 25, 2012 #2


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    You are right.
  4. Oct 25, 2012 #3
    Huh, must be a typo then. Thanks.
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