Truth-Table Example 1
Truth Tables – A Step-By-Step Example
In what follows, the latest additions to the table are given in boldface.
Suppose we are asked to do the truth table for the following statement form:
(1) Q v (P Æ (~Q v ~P))
What follows is a breakdown of the process of building the table for (1).
Step 1: Create the blank table.
There are two atomic statements, P and Q, so the table will have four rows and three columns,
like so (see end of document for more information):
P Q
Q v (P Æ (~Q v ~P))
T T
T F
F T
F F
Step 2: Determine the main connective.
The main connective of (1) is the first occurrence of disjunction (“v”). So the column under this
instance of disjunction will be our ‘final answer’ – our goal is to fill in this column.
Now, in order to figure out what belongs in that main column (under the main connective), we
need to figure out the values for the two disjuncts.
Step 3: Fill in the table.
Figuring out the value for the left disjunct (Q) is easy, because we already have it listed to the
left. So we can simply copy the values over:
P Q
Q v (P Æ (~Q v ~P))
T T
T
T F
F
F T
T
F F
F
Turning now to the right disjunct, we see that it is a compound statement, “P Æ (~Q v ~P)”.
Since it is a conditional, we need to figure out the values for its antecedent and consequent. The
antecedent is easy – it’s just P, and we have the values for P to the left. The consequent is a
disjunction, we need to figure out the values for its two disjuncts, “~Q” and “~P”. Both of these
are negations, so they simply switch True to False and vice versa.
