The four
connectives (or operators) we have
used so far are all binary, meaning they link two distinct
elements. There is also the unary operator for negation (NOT).
Its effect is to reverse the original value of a proposition. For
simplicity, we will not isolate this operator in the following charts
but show its effect in how we color the areas.
The
principal use of truth tables in
symbolic logic is to test for deductive validity. What this
means is that we are trying to determine whether there even is the
possibility that a combination of true premises could imply a false
conclusion. See the difference in the two examples below. The first
represents a pattern that is valid, and the main connective is always
"true." The second represents an invalid pattern, which once has a
"false" main connective. (Think of the main connective--the one for
implication, in this case--as carrying the truth value of the entire
complex proposition.)
