Truth Tables for Logical Operators

These flashcards cover the key concepts related to truth tables and logical operators as discussed in the lecture.

Truth Tables

Diagrams that show when a compound statement is true or false based on the truth values of its sentence variables.

Sentence Variable

A variable that represents a statement that can be either true or false.

Negation

A logical operator that reverses the truth value of a statement (denoted as ~P).

Conjunction

A logical operator that combines two statements and is true only if both statements are true (denoted as P & Q).

Disjunction

A logical operator that combines two statements and is false only if both statements are false (denoted as P V Q).

Conditional

A logical operator that is false only when the antecedent is true and the consequent is false (denoted as P → Q).

Biconditional

A logical operator that is true only if both statements are true or both are false (denoted as P ↔ Q).

Validity

An attribute of an argument where true premises guarantee a true conclusion.

Number of Rows in Truth Table

Calculated as 2 raised to the power of the number of sentence variables.

True/False Distribution

In a truth table, to assign truth values, the first half of the rows are true and the second half are false for the first sentence variable.