Editing Sheffer stroke (section)

==Definition==
The '''non-conjunction''' is a [[logical operation]] on two [[logical value]]s.  It produces a value of true, if — and only if — at least one of the [[proposition]]s is false.

===Truth table===
The [[truth table]] of <math>A \uparrow B</math> is as follows.

{{2-ary truth table|1|1|1|0|<math>A \uparrow B</math>}}

===Logical equivalences===
The Sheffer stroke of <math>P</math> and <math>Q</math> is the negation of their conjunction

{| style="text-align: center; border: 1px solid darkgray;"
|-
| <math>P \uparrow Q</math>
| &emsp;&emsp;<math>\Leftrightarrow</math>&emsp;&emsp;
| <math>\neg (P \land Q)</math>
|-
| [[File:Venn1110.svg|50px]]
| &emsp;&emsp;<math>\Leftrightarrow</math>&emsp;&emsp;
| <math>\neg</math> [[File:Venn0001.svg|50px]]
|}

By [[De Morgan's laws]], this is also equivalent to the disjunction of the negations of <math>P</math> and <math>Q</math>

{| style="text-align: center; border: 1px solid darkgray;"
|-
| <math>P \uparrow Q</math>
| &emsp;&emsp;<math>\Leftrightarrow</math>&emsp;&emsp;
| <math>\neg P</math>
| <math>\lor</math>
| <math>\neg Q</math>
|-
| [[File:Venn1110.svg|50px]]
| &emsp;&emsp;<math>\Leftrightarrow</math>&emsp;&emsp;
| [[File:Venn1010.svg|50px]]
| <math>\lor</math> 
| [[File:Venn1100.svg|50px]]
|}