Logic Exam

Logically Consistent

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

Logically Inconsistent

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

Disjunction

Only false when both disjunctions are false, otherwise it is true.

Conjunction

Only true when both conjunct are true, otherwise it is false.

Negation

Reverses the value.

Logically Contradictory

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

Logically Equivalent

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

Contraction

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

Tautology

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

Contingency

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

(Material) Biconditional

A biconditional is only true when both statements have the same value, otherwise it is false.

(Material) Conditional

A conditional is only false when the antecedent is true and the consequent is false, otherwise it is true.