From owner-cse191-sp08-list@LISTSERV.BUFFALO.EDU  Sun Feb 17 20:22:05 2008
Date:         Sun, 17 Feb 2008 20:21:53 -0500
From: "William J. Rapaport" <rapaport@cse.Buffalo.EDU>
Subject: 191: HW 3
To: CSE191-SP08-LIST@LISTSERV.BUFFALO.EDU

------------------------------------------------------------------------
Subject: 191: HW 3
------------------------------------------------------------------------

A few of you have inquired about problem 10e, the translation of
"Everyone can be fooled by somebody."  This means that, for anyone, there
is someone who can fool him (or her).

Let Fool(x,y) represent "x can fool y".

Then one correct translation would be:

	AxEyFool(y,x)

But another correct translation would be:

	AyExFool(x,y)

Note that, not only are these logically equivalent, but, except for the
change of variable names, they are "notational variants":  They say
exactly the same thing in exactly the same way.

Here is another correct translation that is also just a notational
variant:

	AzEwFool(w,z)

The variable-names don't matter, as long as they are bound by the
correct quantifiers.

This is no different from a computer program:  Two students could have
identical programs that differed only in the names they gave the
variables.  The compiler would compile (or translate) these into exactly
the same machine-language program.  (The students, however, would
probably be correctly accused of plagiarism :-)