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Propositional Logic
Truth Functions

Introduction
Introduction
In 6.1 we symbolized simple statements and
applied operators to natural language in
order to show the logical form of
statements. In this section we will learn how
to assess the truth of logical forms by
defining the operators that compose them.
Last, we will reveal various problems with
our symbolic language in capturing the
meaning of natural language.

Truth-Functional Definitions of
Truth-Functional Definitions of
the Logical Operators
the Logical Operators
Logical operators are functional in that the truth value of
a compound proposition is determined by the truth value
of its components in relation to the definition of the
operator.
The definitions of the logical operators are presented in
terms of statement variables, such as the lower-case
letters p, q, r, and s.
These variables stand for any
possible statement, say A or
∼
(A
•
B).

Statement Forms
Statement Forms
Statement variables are used to construct

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