Boolean Algebra Calculator
Parse and evaluate a boolean expression, enumerate all input combinations, and identify tautologies.
About Boolean Algebra Calculator
Boolean algebra deals with expressions over binary variables using AND, OR, NOT and related operators. This calculator evaluates the expression for every possible input combination to determine satisfiability and tautology status.
Formula
De Morgan's Laws
NOT(A AND B) = (NOT A) OR (NOT B); NOT(A OR B) = (NOT A) AND (NOT B)
- A,B
- Boolean variables
Worked example
With the default values below, Boolean Algebra Calculator returns Satisfiable? of Yes. Change any input above and every figure here is recalculated in your browser.
Inputs used
- Boolean Expression
- A AND (B OR NOT A)
Results
- Satisfiable?
- Yes
- Tautology?
- No
- True assignments
- 1
- Total assignments
- 4
Step by step
- 1Values used
- 2De Morgan's Laws
- 3Satisfiable?= Yes
- 4Tautology?= No
- 5True assignments= 1
- 6Total assignments= 4
Assumptions and limits
- The result is derived only from the single input listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
What does satisfiable mean?
An expression is satisfiable if there exists at least one assignment of truth values to its variables that makes it true.
How does this differ from the truth table generator?
The truth table shows the full table; this focuses on classifying the expression (tautology, satisfiable, contradiction) and counting satisfying assignments.