Editing Logical disjunction (section)

===Defined by other operators===
In [[classical logic]] systems where logical disjunction is not a primitive, it can be defined in terms of the primitive ''[[logical conjunction|and]]'' (<math>\land</math>) and ''[[logical negation|not]]'' (<math>\lnot</math>) as:

:<math>A \lor B =  \neg ((\neg A) \land (\neg B))</math>.

Alternatively, it may be defined in terms of ''[[material conditional|implies]]'' (<math>\to</math>) and ''not'' as:<ref>{{cite book
 |last=Walicki
 |first=Michał
 |author-link=
 |date=2016
 |title=Introduction to Mathematical Logic
 |url=https://www.worldscientific.com/doi/abs/10.1142/9783
 |publisher=WORLD SCIENTIFIC
 |page=150
 |doi=10.1142/9783
 |isbn=978-9814343879
}}</ref>
:<math>A \lor B = (\lnot A) \to B</math>.
The latter can be checked by the following truth table:

{{2-ary truth table
|1|1|0|0|<math>\neg A</math>
|thick
|0|1|1|1|<math>\neg A \rightarrow B</math>
|
|0|1|1|1|<math>A \or B</math>
}}

It may also be defined solely in terms of <math>\to</math>:
:<math>A \lor B = (A \to B) \to B</math>.
It can be checked by the following truth table:

{{2-ary truth table
|1|1|0|1|<math>A \rightarrow B</math>
|thick
|0|1|1|1|<math>(A \rightarrow B) \rightarrow B</math>
|
|0|1|1|1|<math>A \or B</math>
}}

<!-- === Proof theory === -->