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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.

Thanks.

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# Translating English Sentences into Logical Expressions with Nested Quanitifiers

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