Chapter 7

conjuction

a compound statement that has two distinct statements (called conjuncts) connected by the dot symbols

exclusive disjunction

an exclusive disjunction is where both disjuncts cannot be true at the same time

simple statement

one that does not have any other statements as a component

non-contingent statements

statements such that the truth values in the main operator column do not depend on the truth values of the component parts

contingent statements

statements that are neither necessarily true nor necessarily false (they are sometimes true, sometimes false)

biconditonal

a compound statement consisting of two conditionals- one indicated by the word "if" and the other indicated by the phrase "only if." The triple bare symbol is used to translate a bi-conditional statement

disjunction

a compound statement that has two distinct statements (called disjuncts) connected by the wedge symbol

compound statement

a statement that has at least one simple statement as a component

self-contradiction

a statement that is necessarily false

tautology

a statement that is necessarily true

inclusive disjunction

an inclusive disjunction is where both disjuncts can be true at the same time

conditional

in ordinary language, the word "if" typically precedes the antecedent of a conditional. The horseshoe symbol is used to translate a conditional statement

logical operators

special symbols that can be used as part of ordinary language statement translations

propositional logic

the basic components in propositional logic are statements

main operator

the operator that has in its range the largest component or components in a compound statement

truth function

the truth value of a truth-functional compound proposition is determined by the truth value of its components and the definitions of the logical operators involved. Any truth-functional compound proposition that can be determined in this manner is said to be a truth function

negation

the word "not" and the phrase "it is not the case that" are used to deny the statement that follows them, and we refer to their use as negation

inconsistent statements

two (or more) statements that do not have even one line on their respective truth tables where the main operator are true (but they can be false) at the same time

consistent statements

two (or more) statements that have at least one line on their respective truth tables where the main operators are true

contradictory statements

two statements that have opposite truth values on every line of their respective truth tables

logically equivalent

two truth-functional statements may appear different but have identical truth tables. When this occurs, they are logically equivalent