Truth tables for logical expressions
Statements in the propositional logic can only be true or false.
Several statements can be combined with logical connections to new statements.
To show the truth content of such a connection of several statements, one can use a truth table,
which generates all possible combinations of true / false statements and evaluates the corresponding truth content of the logical expression.
In the table logical variables are used instead of concrete statements.
The logical variables used in the expressions can be named as desired.
Allowed operators are (operator priority decreasing in this order):
In addition braces can be used.
|! || "not"||(negation)|
|== || "exactly, when"||(equivalence)|
|&& || "and"||(conjunction)|
||| || "or"||(disjunction)|
Note: The operator priority used here corresponds to the above mentioned programming languages.
In the propositional logic equivalence is weaker than disjunction.
If more than one expression shall be displayed in one table, separating semicolons have to be used.
Example of a logical expression with 4 variables: !a || b && !(c && !d)