exam return and comments...
Next Exam: two weeks! (through chapter four...so we'll get a jump on
that chapter this week)
I. Table review:
A. The idea...one row at a time like
in 3.1 and...
- review the truth table definitions of the connectives,
- think about
- do a couple problems, and
- note how these simple tables lead to the full tables.
B. Full Tables
- Do some,
- think about table length.
II. Concepts and Tables
- It's key to our deductive logic concepts.
- On a table, we list possibilities, each row corresponds to a possibility.
- Definition: Truth value assignments and partial tvas.
We need to
think about possibilities
in terms of ways things could be. For this, we need to give meaning
to our language so that sentences can be true or false given a possibility:
we'll call these interpretations.
B. Logical Truth
- Think about:
- Bob will be a student only if he gets a loan, (B>L),
- If he doesn't get a loan, he won't be a student. (~L>~B).
- There are 4 possible
ways that things
- Logical Truth...the definition revisited:
C. Other concepts...
- Logically False? Indeterminate? Problems!
- Logical Equivalence
For a sentence to be logically equivalent to another
Now, let's see
the definition in
- Here's how to do
one (test to see if 'A=B' is l.equiv. to 'B>(A&B):
- You do:
- ~L>~B vs. B>L
- AvC vs. ~Av~C
- The reference manual
- And other printable pages...under results track.
- But you really need to work through the tutorials.
- Things get more complicated each week. We'll see complicated symbolizations
this week and complications of a new way of doing logic very soon (Chapter
- NO VACATIONS!
Possibility and Logic
- Logical Truth, Falsity, Indeterminacy: A sentence which is...
- Logically True is
true on every
- Logically False
- Logically Indeterminate
- Try some: Which of the following are l.t., l.f. or l.i.?
- Something New:
- Logical Equivalence...
the definition in
- Are the following l.e.?
WvS , ~S>W
IV. The final concepts
Let's work some...
(note this row...)
- "or" revisited.
VI. Informal Proofs: Do each of the following using deductive concepts for SL. (That is, when thinkng about validity, think about valid-in-SL; there is no tva making premises true and conclusion false.)
A. If P entails Q
is valid) then P>Q
is logically true (l.t.).
C. PvQ can
be logically true while both P and Q are logically indeterminate.