If we use a postfix system such as my PLN, truth tables can be a convenient way of showing relationships since the final character holds the value of the entire expression and we can get to it by working from left to right (see the relevant SLIPS sections if you are interested in this--and the DOS programs for creating truth tables are available on request).

With our more traditional infix notation truth tables are less easy to construct and less easy to read.  I suppose this is one reason that many instructors prefer to work with what are called consistency trees instead.  For an Internet course, though, consistency trees do present a different problem, and we will have to do some special programming to work with them easily.

Right now I want to emphasize this idea: our conventional systems of symbolic logic are based on a flip-flop model by which anything we work with must be either one thing (such as "true" or "on") or its opposite ("false" or "off").  This is why they are so useful for mapping what happens with electronic circuits.  It is also why they are useful for mapping what happens with the strictly deductive reasoning by which one statement is seen as "following" from how we express some other statements.

To better understand truth tables I like to work with a flip-flop model based on color (and, later, I'll mention how this concept of colors also allows us to move to a multivalued logic).  The next few screens will give you a chance to see how a game might be played out in which choosing one relationship rather than another (conjunction rather than implication, for instance) different effects can be produced.