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:

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

Truth Table Calculator

Our truth table calculator generates truth tables for propositional logic expressions, allowing you to analyze statements that can only be true or false.

What Is a Truth Table?

A truth table lists all possible input combinations for a logical expression and their corresponding output. It is widely used in mathematics, digital logic design, and computer science to evaluate logical statements.

Propositional Logic Basics

A proposition is a declarative statement with a truth value of either true or false. Propositional expressions are formed using propositional variables (like P, Q, A, B) and logical connectives to combine them into complex statements.

Logical Connectives

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

Propositional Equivalences

Two logical statements A and B are equivalent if:

The bi-conditional A ⇔ B is a tautology.
Their truth tables produce identical results for all input combinations.

Example: Checking Equivalence

Verify that ~(P ∨ Q) is equivalent to (~P ∧ ~Q):

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

As shown, the truth values for ~(P ∨ Q) and (~P ∧ ~Q) match for all input combinations, confirming their equivalence.

Using the Truth Table Calculator

Input:

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

Output:

The calculator produces a truth table for up to four variables and evaluates the expression for every possible combination of truth values.

Conclusion

This online truth table generator helps you quickly create multivariable propositional logic tables. Truth tables are essential for verifying logical equivalences, analyzing expressions, and understanding how statements interact based on their truth values.

References

Wikipedia: Truth table, Logical conjunction (AND), Logical disjunction (OR), Logical negation (NOT), Logical implication, Logical equivalence, Binary operations, Unary operations.