- #1
nicnicman
- 136
- 0
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.
Thanks.
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.