MIME-Version: 1.0
X-Priority: 3
Date:         Thu, 26 Oct 2000 14:53:52 -0400
Reply-To: "IST 230, section 2, fall 2000" 
Sender: "IST 230, section 2, fall 2000" 
From: "David R. Mudgett" 
Subject:      Clarification of Advanced Exercise 4, page 188, HW # 9
To: L-IST230-2@LISTS.PSU.EDU

Hello -

To do this problem, it is necessary to interpret the text authors' statement
of the so-called 'Deduction Theorem',

"If P |- Q, then  |- (P ==> Q)"

where the symbol " |- ", unfortunately, is not defined in the book (at least
as far as I can see.) The statement "  |- P "  stands for "P is a
tautology".  This is written in some logic books as " |= P ".

Hence, I would interpret this statement as

"If (P implies that Q is a tautology), then the sentence (P implies Q) is a
tautology."

Even more to the point, you can proceed by a 3-step process:

1) Assume P.

2) Under this assumption, prove Q.

3) Now, release this assumption, and simply write (P ==> Q).

Hope this helps.

Dave Mudgett