Logic Chapter 7.5

a

(abbreviated truth table stuff)

statements, categories, relationships

Truth tables can be used to sort _ into logically significant _ and to show logically significant _ between statements.

Logically consistent

Two (or more) statements are _ if and only if they are both (all) true on some assignment of truth values to their atomic components

Logically inconsistent

Two (or more) statements are _ if and only if they are never both (all) true on any assignment of the truth values to their atomic components.

Tautology

It is impossible for the conclusion to be false while the premise is true when an argument has a conclusion that is a _.

True

The premises of an argument are inconsistent if there is no row in the truth table in which all of the premises are _

Logically equivalent

Two statements are _ if and only if they agree in truth value on every assignment of truth values to their atomic components.

Logically contradictory

Two statements are _ if and only if they disagree in truth value on every assignment of truth values to their atomic components

Inconsistent triad

Three statements that cannot all be true

Tautology, Contradiction, Contingent

A statement can be a _ or a _. A statement can be _.

Contingent

A statement is _ if and only if it is true on some assignments of truth values to its atomic components and false on others.

Contradiction

A statement is a _ if and only if it is false on every assignment of truth values to its atomic components.

Tautology

A statement is a _ if and only if it is true on every assignment of truth values to its atomic components.

Unsound, False

All arguments having a contradiction among their premises are _ because contradictions are always _.

Contradiction

Any argument that has a _ among its premises is a valid argument.

Logically inconsistent

Any argument with _ premises will be valid yet unsound.

Valid, Unsound

Any argument with logically inconsistent premises will be _ yet _.

Valid

Every argument whose conclusion is a tautology is _, regardless of the content of the premises.

Inconsistent Premises

Every argument with _ is valid.

Valid

Every argument with inconsistent premises is _.

Logically Equivalent

If a biconditional statement is a tautology, then its two constituent statements (joined by the double-arrow) are _.

Inconsistent, Contradiction

If the premises of an argument are _, then if we form a conjunction of the premises, that conjunction will be a _.

Contingent

In a truth table, a statement is _ if it is true on some rows and false on other rows.

Tautology

In a truth table, a statement is a _ if it is true on every row.

false

In a truth table, a statement is a contradiction if it is _ on every row.

true

In a truth table, a statement is a tautology if it is _ on every row.