Subject: HW #5
From: "William J. Rapaport" <rapaport@buffalo.edu>
Date: Tue, 6 Oct 2009 19:32:45 -0400 (EDT)

A student writes:
"Could you do another example for question #1 on the 5th homework for
the first 2 parts:

'For each part, first give the syntax and semantics of translations of
each sentence into the language of propositional logic.'

and

'Then write each argument in your propositional language.'"

Reply:  
I'll do p. 72, #3d, which has the answer in the back of the book.

Argument in English:  
1. If it snows today, the university will close.
2. The university is not closed today.  
3. Therefore, it did not snow today.

"Dictionary" for translation into propositional logic:
Syntax	Semantics
------ --------- 
s	It snows today
u	The university will close.

Argument in propositional logic:  
1. (s -> u)
2. -u
3. Therefore, -s

Rule of inference: Modus Tollens