*   reminder: truth table for IF-THEN,
    P -> Q   (If P, then Q)

    say, for sake of example,
    P = You get an A on the test
    Q = I will give you a dollar

    P -> Q = If you get an A on the test, THEN I will give
             you a dollar

    P    Q    P->Q
   ----------------
    T    T     T
    T    F     F
    F    T     T
    F    F     T

*   EXAMPLE:
    ARGUMENT:
    *   If the train was on time, then the bus
        was not on time.
    *   The bus was on time.
    *   Therefore, the train was not on time.

    *   identify the SIMPLE statements within,
        and label them with letters.

        P = The train was on time.
        Q = The bus was on time.

    *   rewrite the argument in propositional
        logic notation

        P -> ~Q
        Q
        ∴ ~P          

    *   make a TRUTH TABLE to help determine the validity
        of this argument:

        *   SUGGESTION: put (*) above the column of each
            PREMISE, and put (C) above the column for the
            CONCLUSION 
            *   I think text puts to the side of the column
                header, without (), and I'm finding that
                harder to "see"...

           (*)        (*)   (C)
        P   Q   ~Q   P->~Q   ~P
       ------------------------
        T   T    F    F      F
        T   F    T    T      F
        F   T    F    T      T
        F   F    T    T      T

    *   NOW cross out ALL rows for which ANY premise
        is False (done on document camera copy)

	AND see: in the remaining rows, is the
	Conclusion ALWAYS T?
	It IS, here, so this argument *IS* VALID

*   EXAMPLE:
    *   If I have a clean driving record, then I'll receive
        a discount on my auto insurance.
    *   I do have a clean driving record.
    *   So, I'll get the discount.

    *   identify the simple statements,
        and assign each a letter

        P = I have a clean driving record.
        Q = I'll get the auto insurance discount.

    *   rewrite the argument in propositional logic
        form:
        P -> Q
        P
        ∴ Q			

    *   truth table:

       (*) (C)   (*)
        P   Q    P->Q
       ---------------
        T   T     T
        T   F     F
        F   T     T
        F   F     T

    *   NOW cross out ALL rows for which ANY premise
        is False (done on document camera copy)

	AND see: in the remaining rows, is the
	Conclusion ALWAYS T?
	It IS, here, so this argument *IS* VALID

*   EXAMPLE (maybe to be completed Monday)

    (adapted from course text)

    *   Students can raise their grade by studying hard,
        but not by doing extra-credit work.
    *   It's not the case that students can raise their
        grades by doing extra-credit work and hiring
	a tutor.
    *   SO, students can raise their grade
        by studying hard and also by getting a tutor.

    *   IDENTIFY the buried simple statements,
        and assign each a letter!

        S = Students can raise their grade by studying hard
        E = Students can raise their grade by doing
            extra-credit work.
        R = Students can raise their grade by getting a tutor.

    *   rewrite the argument in propositional logic form:

        S ^ ~E
        ~(E ^ R)
        ∴  S ^ R

    *   next: we'll build an appropriate truth table!