*   ONE of our common patterns from Chapter 3:

    categorical syllogism - a 3-line argument in which each
        statement begins with the word ALL, SOME, or NO

*   in Chapter 9, we focus on these;
    *   TOOLS for better reasoning about these
 
    *   CONVERTING categorical statements into so-called
        "standard form" categorical statements

    *   using VENN DIAGRAMS as a means to help reason
        both about categorical statements and
	judging the validity of categorical syllogisms

*   FIRST: categorical *statements*

    *   statements about membership in categories

    *   key words:

        ALL    SOME    NO (meaning none)   NOT

*   THEN: to make reasoning about these easier,
    it is useful to translate suitable statements into
    what's called STANDARD FORM categorical statements

    ONE of these FOUR forms:

    *   ALL A are B.
        *   All members of group A are ALSO members of group B.

        *   some examples of statements that would translate
	    TO "All A are B"
	    *   Anything that is an A is also a B
	    *   A are also B.
            *   Only B are A.
            
    *   NO A are B.
        *   All members of group A are NOT members of group B.

        *   some examples of statements that would translate
	    TO "NO A are B"
            *   Anything that's an A is not a B.
            *   Nothing that is an A is a B.
            *   Not a single A is B.
            *   No B are A. [really?!]

    *   SOME A are B.
        *   AT LEAST ONE member of group A is a member of group B.

        *   some examples of statements that would translate
	    TO "Some A are B"
            *   A few A are B.
            *   Many A are B.
	    *   Most A are B.
	    *   Some B are A.

    *   Some A are NOT B.
        *   AT LEAST ONE member of group A is NOT a member of group B.

        *   some examples of statements that would translate
	    TO "Some A are not B"
            *   A few A are not B.
            *   Many A are not B.
	    *   Not all A are B.
            *   Some A are non-B.

*   intro to VENN DIAGRAMS (in a logic sense)
    *   see posted figures

    *   circle represents a set of things

    *   overlapping circles indicate that the two
        sets are being related to each other
	in some categorical statement

    *   BE CAREFUL -- these are used DIFFERENTLY in determining
        validity of categorical syllogisms than they often are
        in Math or Computer Science!

        *   case in point: when using them to depict a categorical
            statement, you ALWAYS draw them as overlapping,

 	    BUT you then SHADE any of the 4 areas that CANNOT have
	    any elements in them;

            *   see the "Understanding Venn Diagrams" posted figure --
	        the green shading is meant, there, to say that there
		are NO elements in that area, based on the categorical
		statement being depicted;

        *   DOES feel weird when you are used to other means of
	    using these -
	    BUT I think this approach helps in determining validity
            of categorical syllogisms;