Intermediate Logic Lessons 1-5

Propositional Logic

is a branch of formal, deductive logic in which the basic unit of thought is the proposition.

A proposition

is a statement.

A proposition is truth-functional

when its truth value depends upon the truth values of its component parts

A simple proposition

If a proposition has only one component part

A compound proposition

If a proposition has more than one component part

Logical operators

are words that combine or modify simple propositions to make compound propositions.

A propositional constant

is a uppercase letter that represents a single, given proposition.

A propositional variable

is a lowercase letter that represents any proposition.

Negation

is the logical operator that denies or contradicts a proposition.

A truth table

is a listing of the possible truth values for a set of one or more propositions.

A defining truth table

displays the truth values produced by a logical operator modifying a minimum number of variables.

Conjunction

is a logical operator that joins two propositions and is true if and only if both the propositions are true.

Disjunction

is a logical operator that joins two propositions and is true if and only if one or both of the propositions are true.

The conditional operator

asserts that one component (the antecedent) implies the other (the consequent). It is false if and only if the antecedent is true and the consequent is false.

The biconditional operator

is true when both component propositions have the same truth value, and is false when their truth values differ.