truth table

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:

$a$	$b$	$a\vee b$
F	F	F
F	T	T
T	F	T
T	T	T

For $n$ input variables, there will always be $2^n$ rows in the truth table.A sample truth table for “$(a\wedge b)\to c$” would be

(Note that $\wedge$ represents logical and, while $\to$ represents the conditional truth function).

To compute truth tables of expressions, one often proceeds in steps. for instance,to compute a truth table for “$\mathrm{\neg }p\vee (p\wedge q)$, one might proceed as follows:

For reference, here is a truth table of some popular connectives:

For completeness, here are the remaining connectives, excluding trivial connectives whichdepend on only one or none of their arguments: