there’s going to be a certain amount of fiddling around right in here. of course there’s a *better* way but what we’re after is the *easy* way. standards are great that’s why there’s so many *of* ‘em.
any luck? three different symbols, right?
an equal-sign-that-didn’t-know-when-to-stop;
a “left-and-right-arrow”; and a *double* leftrightarrow.
right?
okay. it appears to work on *this* set-up;
no telling what *your* mileage looks like
(just be sure that it *will* vary).
these symbols, then.
these symbols *all* stand for versions of
“two things have the same interpretation”.
there’s already a great deal of confusion
about (what i take to be) the *best-known*
symbol in this class: the *sign of equality*, “=”.
i’ve remarked on this phenomenon before.
but at the “math 366″ level–my current class–
it becomes very important to be very careful to
*distinguish* between various notions of
“means the same thing as”.
but… how?
Bookmarks
Open A Vein (homepage).
e-mail: vlorbik@gmail.comW'press login.
More mathy stuff by me:
Lectures Without Words (drawings mostly)
Community College Calculus (S '09)
Math 148: Precalculus (W '09)
.
Listserv posts: amte (11/98—8/00)... math-teach (6/05—11/06)Alas, gmail.
Carmen.
Buckeye Link.
VK on facebook.
October 6, 2010 at 1:26 pm
\centerline{Math 366}
\centerline{Quiz 2}
\vskip .5in
\parindent=0
{\bf 1.}
Each of the arguments
{\it (a)} through {\it (d)}
is VALID or NOT VALID;
determine which.
For VALID arguments,
name the valid argument
{\it form} (Modus Ponens or
Transitivity,
for example, or [be careful!]
their Universal counterparts).
For arguments that are
NOT VALID, name the
fallacy illustrated
(Converse Error
or Inverse Error,
for example).
\vfil
{\it (a)}
If that’s a thermometer, then I’m Bugs Bunny.
That’s {\it not} a thermometer.
$\bullet$ I’m not Bugs Bunny.
\vfil
{\it (b)}
$t$ is rational or $t$ is irrational.
$t$ is not irrational.
$\bullet t$ is rational.
\vfil
{\it (c)}
$(\forall x \in R) (x \not\in Q}) \rightarrow (x \in \^Q)$
$\sim(t \in \^Q)$
$\bullet \sim(t \not\in Q)$
\vfil
{\it (d)}
If Pigs Fly, then there’s a Sty in the Sky.
There {\it is} a Sty in the Sky.
$\bullet$ Pigs Fly.
\vfil\vfil
{\bf 2.}
Use BOTH of {\it (a)} a Truth Table AND {\it (b)} a sequence
of Equivalences (from the textbook-and-handout list… naming
a justification for each “step”) to prove
the equivalence $p\wedge \sim(q \wedge \sim p) \equiv p$.
\vfil\vfil\vfil\vfil
\vfil\vfil\vfil\vfil\vfil\vfil
\vfil\vfil\vfil\vfil
\vfil\vfil\vfil\vfil\vfil\vfil
\vfil\vfil
\vfil\eject
{\bf 3.}Is Owen in debt?
Create symbols appropriately
(“OM” replacing “Owen is a millionaire”,
for example). Think through the problem
to discover its Answer.
Then {\it justify} your answer with
a sequence of “steps”
written in these symbols
(and appropriate “logic” code);
each consisting of a three-line
(major premise, minor premise,
conclusion) “argument”. Each
{\it premise} of a given step
should come from the given
information ({\it (a)}–{\it (e)})
or a previous “step”; each
{\it conclusion} will (of course!)
be an instance of some valid
Rule of Inference.
(Compare “Example 2.3.8″ at
Epp, {\it pp.} 56{\it f}).
{\it a.} Owen is a millionaire or Owen is underinsured.
{\it b.} If Owen is underinsured, then Owen is in debt.
{\it c.} If Owen is a millionaire, then Owen is {\it not} in debt.
{\it d.} If Owen is a millionaire, Owen has quit his job.
{\it e.} Owen has not quit his job.
\vfil\vfil\vfil\vfil\vfil\vfil\vfil\vfil\vfil\vfil\vfil\vfil
{\bf 4.}
Write appropriate negations.
It does {\it not} suffice simply to
affix “$\sim$” (or the phrase
“it is not the case that…”
[for example]); the negation
of $x<17$ isn't $\sim(x<17)$,
for example [or $x\not<17$
for that matter], but $x \ge 17$.
\vfil
$\bullet (\forall x) P(x) \rightarrow Q(x)$
\vfil
$\bullet x<0$ or $x\ge 1$
\vfil
$\bullet$ There ain't no life nowhere.
\vfil\eject
\bye
October 7, 2010 at 1:19 pm
http://pdfcast.org/pdf/366q2-pdf
http://www.scribd.com/doc/22921670/Lecture-Notes