| F | F |
| F | T |
| T | F |
| T | T |
 | This is the template sandbox page for Template:2-ary truth table (diff). |
 | This template uses Lua: |
 | This template uses TemplateStyles: |
Usage edit
This template is for articles like Exclusive or. The colors white and red correspond to Venn diagrams like File:Venn0110.svg, as well as other files like File:Variadic logical XOR.svg.
{{2-ary truth table|0|1|1|0|<math>A \oplus B</math>}}
| F | F | F |
| F | T | T |
| T | F | T |
| T | T | F |
More complex tables can be created with the same styles:
- Implications
{{2-ary truth table|A=P|B=Q
|1|1|0|1|<math> P \rightarrow Q</math>
|thick
|1|0|1|1|<math> P \leftarrow Q</math> (converse)
}}
| (converse) | |||
|---|---|---|---|
| F | F | T | T |
| F | T | T | F |
| T | F | F | T |
| T | T | T | T |
- Disjunction with implication
{{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>
}}
| F | F | T | F | F |
| F | T | T | T | T |
| T | F | F | T | T |
| T | T | T | T | T |
- Disjunction with implication and negation
{{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>
}}
| F | F | T | F | F |
| F | T | T | T | T |
| T | F | F | T | T |
| T | T | F | T | T |
In this template A is 0011, and B is 0101. In the corresponding Venn diagram files it is the other way round.
E.g. implication has to be entered as 1101. But the corresponding Venn diagram is File:Venn1011.svg
