Editing False (logic) (section)

=== [[Truth table|Truth Tables]] ===
Sources:<ref>Gottlob Frege (1879, Begriffsschrift)</ref><ref>Alfred Tarski (1930s, Introduction to Logic, Chapter II (Symbolic Logic))</ref>

==== Negation (¬) ====

{| class="wikitable" style="text-align: center"
|-
!<math>x</math>
!<math>\neg x</math>
|-
!true
|false
|-
!false
|true
|}

The negation of false is equivalent to the truth not only in classical logic and Boolean logic, but also in most other logical systems, as explained below.

==== Conjunction (AND ∧) ====

False ∧ True = False (False AND anything is False).

==== Disjunction (OR ∨) ====

False ∨ True = True (OR is True if at least one operand is True).

==== Implication (→) ====

False → True = True (A false premise makes the implication vacuously true).