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Posting-Version: version nyu B notes v1.5 12/10/84; site acf4.UUCP
Path: utzoo!linus!philabs!cmcl2!acf4!hkr4627
From: hkr4627@acf4.UUCP (Hedley K. J. Rainnie)
Newsgroups: net.auto
Subject: Re: Speed, H.P., and Corvettes
Message-ID: <330038@acf4.UUCP>
Date: Fri, 26-Apr-85 20:36:00 EDT
Article-I.D.: acf4.330038
Posted: Fri Apr 26 20:36:00 1985
Date-Received: Sun, 28-Apr-85 05:48:27 EDT
References: <330035@acf4.UUCP>
Organization: New York University
Lines: 68

Response 3 reads:

" I'm obviously missing something here.  My problem is with the last sentence.
  I can see how a car would be unable to redline in top gear.  But how could
  any car be unable to redline in all gears?  If seems like one could easily
  hit 6400 rpm in first before they ever approached 130 mph.  Someone please
  point out the fault in my logic"

  From: rdz@ccice5.UUCP (Robert D. Zarcone)

I'll try.

Where: rx - able to redline in xth gear,

You're thinking:

~r1 * ~r2 * ~r3 * ~r4      (1)
= ~(r1 + r2 + r3 +r4)      (2)

where I was thinking:

~(r1 * r2 * r3 *r4)        (3)

where: + logical or
       * logical and
       ~ negation

Now, I would consider your thoughts to be closer to 
"unable to redline in ANY gear."  One might make the case that
the word ANY implies OR, and the word all implies AND.  For example,
"ALL the  Cleavers" would become "Ward AND June AND Theodore AND Wally"
whereas "ANY of the Cleavers" would be "Ward OR Jun OR Theodore OR Wally"

So, we expand "unable to redline in all gears" to
"unable to redline in 1st and 2nd and 3rd and 4th"
Let's distribute redline:
"unable to redline in 1st and redline in 2nd and redline in 3rd and
redline in 4th"
Now YOU distributed UNABLE, and by doing so:
"unable to redline in 1st and unable to redline in 2nd and
unable to redline in 3rd and unable to redline in 4th."
which is equivalent to (1).  
You assumed that "UNABLE" binds more closely than "ALL".  I disagree.
If we apply DeMorgan's to (1), we get (2) which reads:
"Unable to redline in first or second or third or fourth."  Replacing
the ORs with the ANY structure, you get:
"Unable to redline in any gear."  Which is what you meant.

But!
If you bind the "ALL" first, that is, the gears, you get the unable
stuck outside and something resembling (3).  This can be expressed
"unable to redline in 1st and redline in 2nd and redline in 3d and
redline in 4th."  I.e., there exists a gear such that one cannot
redline the motor while in it."
(3) is the meaning 
I intended to convey.  I think that ALL and ANY always bind first 
since they are abbreviations for AND and OR, respectively.

Since the sentence IS confusing AND there's no reason to bring in the
three lower gears since if the car will redline in top, it will in lower
gears, AND since there is a typo in the original, let's change the sentence
to read:

"In every review I've ever seen, the older Vettes had no trouble redlining
in top gear."

(signed)
speed racer