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Truth Table Generator

Enter one or more sentences of truth-functional logic in the space below. Separate multiple sentences with commas.

Truth-Values:



Logical Operators:



Table Type:



Use the following symbols for the logical operators.

~for negation
&for conjunction
vfor disjunction
->for the conditional
<->for the biconditional
#for absurdity
|for NAND (the Sheffer Stroke)
!for NOR (Wittgenstein's Sheffer Stroke)

These are some examples of well-formed inputs that the program will accept.

~P
(P & Q)
(P & (~Q -> S))
(# -> (Q v ~P))
(P|Q) <-> ~(P & Q)
(P <-> (Q v S)), P, (~Q -> S)

A sentence of TFL is a tautology if and only if it is true on every truth-value assignment. (I.e., there is a “T” on every line below the main logical operator.)

An argument, P1, P2, ... ⊢ C, is valid when ((P1 & P2) & ...) → C is a tautology.

Two sentences, A and B, are equivalent when (A ↔ B) is a tautology.


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