PROPOSITIONAL LOGIC III: TRUTH TABLES FOR PROPOSITIONS AND
ARGUMENTS
Constructing Truth Tables
Step #1: construct a table with the proposition(s) to be assessed to the right of the
dividing line and each of the simple propositions contained therein to the left in
alphabetical order. A truth table with n simple propositions will require 2n rows.
Step #2: in the column under the simple proposition immediately to the left of the
dividing line, place alternating T’s and F’s; in the column under the proposition
2nd to the left of the dividing line, place alternating pairs of T’s and F’s (i.e, T, T,
F, F, T, T, F, F, …); continuing to the left, under each subsequent column double
the number of alternating T’s ad F’s
Step #3: determine the truth-value(s) of the proposition(s) to be assessed for each
truth-value assignment (= each row) by determining the truth-values of the
simpler components on each assignment and working outwards
Evaluating Arguments
Procedure: construct a truth-table with the premises and the conclusion of the
argument to the right of the dividing line placing a single slash (“/”) between each
premise and a double slash (“//”) between the last premise and the conclusion
Valid: an argument is valid if there is no truth-value assignment which makes all
of the premises true and the conclusion false
Invalid: an argument is invalid if there is at least one truth-value assignment that
makes all of the premises true and the conclusion false