Chapter 7 Flashcards
Logical operators:
Special symbols that are used to translate ordinary language statements.
Simple statement:
One that does not have any other statement or logical operator as a component.
Compound statement:
A statement that has at least one simple statement and at least one logical operator as components.
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.”
Conjunction:
A compound statement that has two distinct statements (called conjuncts) connected by the dot symbol.
Disjunction:
A compound statement that has two distinct statements (called disjuncts) connected by the wedge symbol.
Inclusive disjunction:
When we assert that at least one disjunct is true, and possibly both disjuncts are true. Given this, an inclusive disjunction is false when both disjuncts are false, otherwise it is true.
Exclusive disjunction:
When we assert that at least one disjunct is true, but not both. In other words, we assert that the truth of one excludes the truth of the other. Given this, an exclusive disjunction is true when only one of the disjuncts is true, otherwise it is false.
Conditional statement:
In ordinary language, the word “if” typically precedes the antecedent of a conditional statement, and the statement that follows the word “then” is referred to as the consequent.
Sufficient condition:
Whenever one event ensures that another event is realized.
Necessary condition:
Whenever one thing is essential, mandatory, or required in order for another thing to be realized
Biconditional:
A compound statement made up of two conditionals—one indicated by the word “if” and the other indicated by the phrase “only if.”
Sufficient condition:
Whenever one event ensures that another event is realized. In other words, the truth of the antecedent guarantees the truth of the consequent.
Necessary condition:
Whenever one thing is essential, mandatory, or required in order for another thing to be realized. In other words, the falsity of the consequent ensures the falsity of the antecedent.
Well-formed formula:
Any statement letter standing alone, or a compound statement such that an arrangement of operator symbols and statement letters results in a grammatically correct symbolic expression.
Scope:
The statement or statements that a logical operator governs.
Main operator:
The operator that has the entire well-formed formula in its scope.
Truth-functional proposition
The truth value of any compound proposition using one or more of the five operators is a function of (that is, uniquely determined by) the truth values of its component propositions.
Statement Variable:
A statement variable can stand for any statement, simple or compound.
Statement form:
In propositional logic, an arrangement of logical operators and statement variables such that a uniform substitution
Argument form:
In propositional logic, an argument form is an arrangement of logical operators and statement variables such that a uniform substitution of statements for the variables results in an argument.
Substitution instance:
A substitution instance of a statement occurs when a uniform substitution of statements for the variables results in a statement. A substitution instance of an argument occurs when a uniform substitution of statements for the variables results in an argument.
Truth table:
An arrangement of truth values for a truth-functional compound proposition that displays for every possible case how the truth value of the proposition is determined by the truth values of its simple components.
Truth function:
The truth value of a compound proposition is a function of the truth values of its component statements and the logical operators
