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Truth Table Calculator

Enter any logical formula, and this calculator will instantly generate the complete truth table.

Enter an Equation:

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

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Truth Table Calculator:

This truth table calculator instantly generates complete truth tables for any logical or Boolean expression. Enter your formula, and the calculator evaluates all possible input combinations to compute outputs for every row, displaying step-by-step results for better understanding. It supports all standard operators, including AND (\(\land\)), OR (\(\lor\)), NOT (\(\neg\)), XOR (\(\oplus\)), NAND, NOR, XNOR, and Implication (\(\rightarrow\)). Fast, accurate, and ideal for students, teachers, programmers, and anyone analyzing Boolean logic.

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.

How To Use the Truth Table Calculator?

Follow these steps:

Input:

Enter a propositional logic formula using standard logical symbols (AND "\(\land\)", OR "\(\lor\)", NOT "\(\neg\)", etc.)

Action:

Click “Calculate” to generate the truth table instantly.

Output:

The calculator produces a truth table for up to four variables, showing the evaluated result 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.

Reference:

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

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