Boolean Algebra Calculator

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Enter a boolean expression such as A ^ (B v C) in the box and click Parse.

Supported operations are AND, OR, NOT, XOR, IMPLIES, PROVIDED and EQUIV.

Operations and constants are case-insensitive.

Variables are case sensitive, can be longer than a single character, can only contain alphanumeric characters, digits and the underscore character, and cannot begin with a digit.


Operations are executed in order of precedence, from higher to lower. Operations with the same precedence are executed from left to right. To execute a particular operation first, surround it with parenthesis ( ).

Operation Aliases Evaluates to true if Evaluates to false if Precedence
NOT A ~ ' ! ¬ A is false. A is true. highest
A AND B ∧ ^ & · * both A and B are true. either or both are false. middle
A EQUIV B ⇔ ≡ ↔ = both A and B are true; or both are false. one is true and the other is false. middle
A IMPLIES B ⇒ → ⊂ < A is false; or A is true and B is true. A is true and B is false. middle
A PROVIDED B ⇐ ← ⊃ > A is true and B is true; or B is false. A is false and B is true. middle
A OR B ∨ v + ∥ | A is true; B is true; or both are true. both are false. lowest
A XOR B ⊻ ⊕ A is true and B is false;
or A is false and B is true.
both are true or both are false. lowest


Constant Aliases Description
TRUE 1 T ⊤ true Always evaluates to true.
FALSE 0 F ⊥ false Always evaluates to false.