USING TRUTH TABLES TO DO LOGIC
TASKS IN PROPOSITIONAL LOGIC
Sandra
LaFave
To
determine whether or not a statement is a tautology:
 Construct
a complete truth table
 Inspect
the column under the main operator
 If the
column under the main operator contains all T’s, the statement is a
tautology.
To
determine whether or not a statement is a selfcontradiction:
 Construct
a complete truth table
 Inspect
the column under the main operator
 If the
column under the main operator contains all F’s, the statement is a
selfcontradiction.
To
determine whether or not a statement is a contingency:
 Construct
a complete truth table
 Inspect
the column under the main operator
 If the
column under the main operator contains mixed T’s and F’s, the statement
is a contingency. The “T” rows show
the conditions under which the statement comes out true; the “F” rows show
the conditions under which the statement comes out false.
To
determine whether or not two statements are logically equivalent:
 Construct
complete truth tables for both statements.
 Inspect
the columns under the main operators.
 If the
columns under the main operators are identical (same Ts and Fs for every
row), the statements are logically equivalent.
To
determine whether or not two statements are contradictories:
 Construct
complete truth tables for both statements.
 Inspect
the columns under the main operators.
 If the
columns under the main operators are exactly opposite (different truth
values for every row), the statements are contradictories.
To
determine whether or not a set of statements is consistent:
 Construct
complete truth tables for all the statements.
 Inspect
the columns under the main operators.
 If there
is a row of all the truth tables in which the main operator of each
statement is true, the statements are consistent, i.e., it is possible
that they might all be true. The
line(s) in which the statements all come out true shows the conditions
under which the statements can be all true.
To
determine whether or not a set of statements is inconsistent:
 Construct
complete truth tables for all statements.
 Inspect the
columns under the main operators.
 If there
is no row of all the truth tables in which the main operator of each
statement is true, the statements are inconsistent, i.e., it is impossible
that they might all be true.
To
determine if an argument is valid:
 Translate
from English if necessary
 Write the
premises and conclusion horizontally, premises on left, conclusion on
right. Order of premises does not
matter.
 Do
complete truth table. (Or use short
cut method.)
 Inspect
the truth table. Is there any row
in which premises all come out true and conclusion comes out false? If yes, argument is invalid. If no, argument is valid.
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