MAT 1348 Study Guide - Final Guide: Propositional Calculus, Automated Reasoning, Propositional Variable
Lecture 1
Propositional Logic
We need to understand the rules of logic in order to understand and
evaluate mathematical statements.
These rules form the basis of automated reasoning (think of com-
puter science).
To understand propositional logic we need some terminology.
Proposition: a declarative sentence that is either true (T) or false
(F), but not both.Tand Fare called the truth values. (The truth
value of a proposition cannot be ambiguous.)
(Note for the curious: There are diļ¬erent types of logic where there
are more than two truth value options for a given proposition. See
āfuzzy logicā for example.)
Examples:
Propositional variable: a symbol (conventionally one of the let-
ters p, q, r, s,. . .) that represents an unknown proposition.
1
Document Summary
We need to understand the rules of logic in order to understand and evaluate mathematical statements. These rules form the basis of automated reasoning (think of com- puter science). To understand propositional logic we need some terminology. Proposition: a declarative sentence that is either true (t) or false (f), but not both. Propositional variable: a symbol (conventionally one of the let- ters p, q, r, s, . that represents an unknown proposition. Logical connectives are operators used to connect multiple propo- sitions, thereby forming a compound proposition. We want to be able to assign a truth value to a given compound proposition. In fact, the truth value of a compound proposition com- pletely depends on the truth values of the ingredient propositions. To cover all possible scenarios for the truth values of the ingredient propo- sitions we construct a truth table. Consider a compound proposition q that involves ingredient propo- sitions denoted by the propositional variables p1, p2, .