Before we discuss the specifics of filling in truth
tables, click here
if the characters in your truth tables do not look
properly aligned in columns.
Completing a Truth Table
Upon selecting a truth table exercise, one is
presented with an incomplete truth table like this one:
The top line of the incomplete truth table contains
the statement letters contained in the argument, a
vertical line, and the sentence or argument for which
the truth table is to be constructed. The next line
contains a separator  basically a row of hyphens and a
single vertical line. Beginning on the third line,
beneath the statement letters appear the 2^{n}
possible distinct truth value assignments that can be
given for the statement letters. (Because there is such
a simple algorithm for constructing these truth value
assigments, we decided to relieve you of the tedium of
constructing them yourself  but be sure you know
how to construct them on your own! You will need to
know how to to do this on your exams.) To complete each
row correctly, follow these two guidelines:
 Enter a truth value (i.e., T or F)
under each logical operator.
 Enter a truth value beneath an occurrence of a
statement letter if, and only if, that
occurrence of the statement letter is either one of
the premises of the argument or its conclusion .
Thus, following these guidelines a correct first row
will look like this:
Filling out each row in similar fashion, a completed
truth table will look something like this:
Clicking on the `Check Truth Table Now!' button will
do just that, i.e., it will check to see that you have
filled in the truth table correctly. If you have not,
you should get a helpful response telling you what went
wrong, and a copy of your truth table in a new box in
which you can make the necessary corrections.
Determining Validity
Once your truth table is correct, you will be
presented with a page that asks you to assess its
validity. The relevant portion of the page looks like
this:
As noted in Section 7.3 of the text, to test for
validity, you look to see whether or not there is a row
of the table on which the premises of the argument are
true and the conclusion false. If you do not find such a
row, the argument is valid, so click on the `Valid'
button to complete the exercise. If you have missed such
a row you will be so informed and presented with your
errant truth table for you to fix. If you do find such a
row, check the checkbox to its left, as indicated in our
example:
You may then either click on the `Invalid' button
(one row with true premises and false conclusion is all
you need to establish invalidity) or you may continue to
search for further invalidating rows. If the row you
check is invalidating, but you miss further invalidating
rows, the program will tell you your answer is correct,
but will give you the opportunity to find the
invalidating rows that remain. In either case, if you
have checked a row that does not invalidate the
argument, you will again be so informed and presented
with your errant truth table. If you are correct, enjoy
the praise that will be heaped upon you!

The Power of Logic
Exercise 7.3A Problem 25 
Correct!
You are correct! Row 3 shows that
the argument is invalid! On this row of
the truth table, the premises of the
argument are true and the conclusion
false. 
Your truth table:
A B  ~A > (~B > A), B :. ~~A

T T  F T F T T TF
T F  F T T T F TF
F T  T T F T T FT
F F  T F T F F FT


Appearance Problems in Netscape
If you are using Netscape, and
statement letters, vertical bars, and truth values (T's
and F's) do not seem to be lining up properly
in columns, then Netscape is probably not paying
attention when it is being told to use a "nonproportional"
font in a text area. The problem is that Netscape by
default likes to use a "proportional" font in text
areas, that is, a font whose characters come in
different widths. Thus, in a proportional font like
Times or Helvetica, an "m", for example, will usually be
a lot wider than an "i" or a "". To fix this problem,
click on the "Edit" menu option and then click on
"Preferences...". In the dialog box that comes up, click
on the little icon next to "Appearance" so you can see
its suboptions, and then click on "Fonts". Depending on
whether you are using Netscape 4 or Netscape 6, do one
of the following:
 In Netscape 4, on the right side of the dialog
box you should find that the button next to the
option to "Use my default fonts, overriding
documentspecified fonts" has been clicked. Click on
either of the other options which begin "Use
documentspecified fonts".
 In Netscape 6, on the right side of the dialog
box you will simply find a checkbox option to "Allow
documents to use other fonts". Check that option.
This procedure should allow Netscape to obey when it is
told to use a nonproportional font, and hence should now
render beautiful truth tables! 