Truth Table Calculator

Truth Table Calculator

Write down a logical formula and the calculator will instantly compute truth table values for it, with the steps shown.

Enter an Equation:

Symbols
Negation	~
Conjunction (AND)	&
Disjunction (OR)	v
Conditional	->
Biconditional	<->
Sheffer Stroke	\|
Absurdity	#

Truth Table Calculator

This truth table calculator generates truth table values for given propositional logic formulas. In propositional logic, statements can only be true or false.

What is a Truth Table?

A truth table is a tabular representation of all possible input combinations and their corresponding outputs for a logical expression. It is used in mathematics, logic algebra, and electronic circuits to visualize and analyze the behavior of logical statements.

Propositional Truth Tables Logic

A proposition is a declarative statement with a truth value of either true or false. Propositional expressions are composed of propositional variables and connectives. Capital letters (A, B, P, Q, etc.) typically represent propositional variables. Connectives link these variables to form logical expressions.

How to Make a Truth Table?

Connectives Used in Propositional Logic

OR (∨)
AND (∧)
Negation / NOT (¬)
Implication / If-Then (→)
If and Only If (⇔)
Absurdity (#)
Sheffer Stroke (|)

Propositional Equivalences

Two statements A and B are logically equivalent if one of the following conditions holds:

The bi-conditional statement A ⇔ B is a tautology.
The truth tables for both statements produce identical truth values for all input combinations.

Example: Verifying Equivalence

Prove that ~(P ∨ Q) and (~P ∧ ~Q) are equivalent.

P	Q	P ∨ Q	¬(P ∨ Q)	¬P	¬Q	(~P ∧ ~Q)
T	T	T	F	F	F	F
T	F	T	F	F	T	F
F	T	T	F	T	F	F
F	F	F	T	T	T	T

Here, the truth values of ~(P ∨ Q) and (~P ∧ ~Q) match for all combinations of P and Q, confirming that the statements are equivalent.

How Does the Truth Table Calculator Work?

Input:

Enter a propositional logic formula using standard symbols.
Click the “Calculate” button to generate the truth table.

Output:

The calculator constructs a truth table for up to four variables and evaluates the expression for all possible combinations.

Conclusion

Use this online truth table generator to create multivariate propositional logic truth tables quickly. Propositional logic deals with statements that can only have truth values of true or false. Truth tables help analyze these statements individually or collectively.

References

Wikipedia: Unary operations, Logical true, Logical false, Truth table, Logical identity, Logical negation, Binary operations, Logical conjunction (AND), Logical disjunction (OR), Logical implication.