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A truth table is a tabular listing of all possible input value combinations for a logical function and their corresponding output values. Similarly, the truth table of a logical proposition is the truth table of the corresponding logical function.
For instance, the truth table of the connective “or” is as follows:
For  input variables, there will always be  rows in the truth table. A sample truth table for “
 ” would be
 |
 |
 |
 |
| F |
F |
F |
T |
| F |
F |
T |
F |
| F |
T |
F |
T |
| F |
T |
T |
F |
| T |
F |
F |
T |
| T |
F |
T |
F |
| T |
T |
F |
T |
| T |
T |
T |
T |
(Note that  represents logical and, while
 represents the conditional truth function).
To compute truth tables of expressions, one often proceeds in steps. for instance, to compute a truth table for “
 , one might proceed as follows:
 |
 |
 |
 |
 |
| F |
F |
T |
F |
T |
| F |
T |
T |
F |
T |
| T |
F |
F |
F |
F |
| T |
T |
F |
T |
T |
For reference, here is a truth table of some popular connectives:
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 |
 |
 |
 |
 |
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| F |
F |
F |
F |
F |
T |
T |
| F |
T |
T |
F |
T |
T |
F |
| T |
F |
T |
F |
T |
F |
F |
| T |
T |
T |
T |
F |
T |
T |
For completeness, here are the remaining connectives, excluding trivial connectives which depend on only one or none of their arguments:
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 |
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|
|
| F |
F |
T |
T |
T |
F |
F |
|
|
| F |
T |
T |
F |
F |
F |
T |
|
|
| T |
F |
T |
F |
T |
T |
F |
|
|
| T |
T |
F |
F |
T |
F |
F |
|
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