Boolean Algebra Calculator
Parse and evaluate a boolean expression, enumerate all input combinations, and identify tautologies.
Inputs
Operators: AND, OR, NOT, XOR, IMPLIES. Max 6 variables.
Satisfiable?
Yes
Tautology?
No
True assignments
1
Total assignments
4
Step by step
Values used
Boolean Expression = A AND (B OR NOT A)
De Morgan's Laws
NOT(A AND B) = (NOT A) OR (NOT B); NOT(A OR B) = (NOT A) AND (NOT B)
Satisfiable?
= Yes
Tautology?
= No
True assignments
= 1
Total assignments
= 4
How it works
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
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.