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Currently (May 2018) the pages for the Logical Connectives are a mess of competing styles and presentations, which hinders comprehension. I propose this style guide to define a common presentation for all the boolean connectives.
The article Logical connectives, and the articles
With exception to Negation and Material Conditional, as they have a more general scope.
<math>...</math>
to display logical formulas.In general,
Sheffer stroke | Prefer to |
Converse implication | Prefer to |
Implication | Prefer to |
Disjunction | Prefer to |
Negation | Prefer to , or |
Exclusive or | Prefer to , or |
Biconditional | Prefer to , or |
Joint denial | Use |
Material nonimplication | Prefer to |
Converse nonimplication | Prefer to |
Logical conjunction | Prefer to , , or |
For boolean connectives the table should look like
T | T | ? |
T | F | ? |
F | T | ? |
F | F | ? |
using T and F for the truth-values, and without the headings "Input" and "Output", as a boolean connective expresses a relation, not a computation.
For logic gates, the truth table should look like
Input | Output | |
A | B | A OP B |
0 | 0 | ? |
0 | 1 | ? |
1 | 0 | ? |
1 | 1 | ? |
using 1 and 0 as the truth-values, and starting with "0 0" at the top.
(This appears to be the style used in the articles on logic gates; I would prefer to start with "1 1", but there may be some reason I'm not aware of that they start with "0 0")
Engineering notation is recommended when writing formulae for logic gates.
<math>...</math>
Disjunction | Use |
Negation | Use , not |
Exclusive or | Use |
Logical conjunction | Prefer over , except when used for emphasis |