For instance, the truth table of the connective
“or” is as follows:
| a |
b |
a∨b |
| F |
F |
F |
| F |
T |
T |
| T |
F |
T |
| T |
T |
T |
For n input variables, there will always be 2n rows in the truth table. A sample truth table for “(a∧b)→c” would be
| a |
b |
c |
(a∧b)→c |
| 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 |
To compute truth tables of expressions, one often proceeds in steps. for instance, to compute a truth table for “¬p∨(p∧q), one might proceed as follows:
| p |
q |
¬p |
(p∧q) |
¬p∨(p∧q) |
| 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:
| p |
q |
p∨q |
p∧q |
p⊻q |
p→q |
p↔q |
| 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:
| p |
q |
p∧q |
p∨q |
p←q |
p↛q |
p←q |
| 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 |
| Title |
truth table |
| Canonical name |
TruthTable |
| Date of creation |
2013-03-22 11:54:35 |
| Last modified on |
2013-03-22 11:54:35 |
| Owner |
rspuzio (6075) |
| Last modified by |
rspuzio (6075) |
| Numerical id |
16 |
| Author |
rspuzio (6075) |
| Entry type |
Definition |
| Classification |
msc 03-00 |
| Classification |
msc 34C29 |
| Related topic |
ZerothOrderLogic |
| Related topic |
PropositionalCalculus |