DISJUNCTIONS

        A disjunction asserts that at least one of two statements is true.
The two statements are called the disjuncts of the disjunction.  The
disjunction is represented by the symbol 'v' which reads 'or'.  It is a
common misconception to read this 'or' as an exclusive-or.  The
exclusive-or says that one of two statements is true and the other is
false.  The logical-or is non-exclusive.  The or-statement (P v Q), for
instance, is true even if both P and Q are true.  The truth table for the
disjunction is given in the answer to problem II. from the homework.  You
should note that (P v Q) is logically equivalent to ~(~P & ~Q), from
problem I.

        CONDITIONALS

        A conditional asserts that one statement is true if another
statement is true.  It is typically expressed by "if ... then ...", but it
does not carry all the conotations that "if ... then ..." usually carries.
For instance, I might say "If I had a billion dollars, I would be a
pauper."  As we typically use "if ... then ..." that statement is false.
But the conditional (B -> P), where B means I have a billion dollars, and P
means I am a pauper, is true.  This is because the '->' represents nothing
more than a relationship between the truth values of two statements.  We
call the statement before the '->' the antecedent, and we call the
statement after the '->' the consequent.  The conditional merely asserts
that the consequent is true if the antecedent is true.  Thus, a conditional
is true whenever the antecedent is false.  The truth table for the
conditional looks like this:

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

        You may note that the conditional is logically equivalent to ~(P &
~Q), which I gave a truth table for in lesson two.  It is also equivalent
to (~P v Q).

        BICONDITIONALS

        A biconditional asserts that the two statements it connects have
the same truth value.  It gets its name because it is equivalent to [(P ->
Q) & (Q -> P)].  The truth table for the biconditional looks like this:

        P   Q   (P <-> Q)
        -----------------
        T   T       T
        T   F       F
        F   T       F
        F   F       T