Truth Table Generator

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

Truth-Values:

T/F
⊤/⊥
1/0

Logical Operators:

¬, &, ∨, →, ↔
¬, ∧, ∨, →, ↔
~, &, ∨, ⊃, ≡

Table Type:

Full Table
Main Connective Only
Text Table
LaTex Table

Use the following symbols for the logical operators.

~	for negation
&	for conjunction
v	for 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.

The source code for this webpage is available on Github.