Tautologies and Contradictions

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Tautologies and Contradictions Truth Tables with
Three Propositions Testing the Validity of
Simple Arguments Using Truth Tables
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A tautology is a compound proposition that is
always true regardless of the truth values of the
individual propositions.
Show that the compound proposition If p, then or
q is a tautology.
All the final entries are T so the proposition
is a tautology.
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A contradiction is a compound proposition which
is always false regardless of the truth values of
the individual propositions.
Show that the compound proposition p and not p
is a contradiction.
All the final entries are false so the
proposition is a contradiction.
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Truth Tables Involving Three Propositions
Truth tables can be extended to deal with any
number of propositions, but IB will limit the
number to three.
Your truth table should start with the three
columns at the left.
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Construct at truth table to show all the truth
values of the compound proposition
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Testing the Validity Using Truth Tables
An argument is made up of one or more premises
that lead to a conclusion. The premises and the
conclusion are propositions. If the premises
provide support for the conclusion then the
argument is said to be valid. The conclusion of
an argument can be identified as it is introduced
by words such as therefore ( ), hence, so,
it follows.
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Prove If Fuzzy is a bear then Fuzzy is a mammal.
Fuzzy is a bear. Therefore fuzzy is a mammal.
The argument can be written in logical form in
the following way. If Fuzzy is a bear then fuzzy
is a mammal. Fuzzy is a bear. p These two
propositions combined The premises logically
imply the conclusion The argument is valid if
the truth values of the logic statement from a
tautology. Create a truth table to prove the
argument is valid.
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Therefore the argument is valid because the
compound proposition is a tautology.
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Discuss the validity of the argument If Julia is
sick she will not go to work. Julia is not sick
. Therefore Julia will go to work.
Write statements for each of the following
symbols
p
q
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Since the compound proposition is not a tautology
the argument is invalid.