This calculator creates a
*truth table*
for any logical expression. To get started, enter the boolean expression into the calculator.

Truth table calculator

Install calculator on your site

Calculator supports the following logical operations:

This operation is denoted by the
symbol. To enter it into our calculator, one can use either ¬ symbol or symbol of exclamation mark (!). The negation operation is unary (contains one operand only) and have the highest priority among the logical operations.

The truth table of logical operation "not" has the form:

This operation is denoted by the
symbol. To enter it into our calculator, one can use either ∧ symbol or two ampersand (&&) symbols. The conjunction operation is binary (contains two operands).

The truth table of logical "and" operation has the form:

This operation is denoted by the
symbol. To enter it into our calculator, one can use either ∨ or two || symbols. The disjunction operation is binary.

The truth table of the logical "or" operation has the form:

This operation is denoted by the
symbol. To enter it into our calculator, one can use either ⊕ symbol or a function
.

The truth table of logical "exclusive or" operation has the form:

This operation is denoted by the
symbol. To enter it into our calculator, one can use either ↑ or | symbol.

The truth table of logical operation "not and" has the form:

This operation is denoted by the
symbol. To enter it into our calculator, one can use either ↓ symbol or a function
.

The truth table of logical "not or" has the form:

This operation is denoted by the
symbol. To enter it into our calculator, one can use either ⇔ symbol or <=> (less sign, equal sign, greater sign) construction.

The truth table of logical equivalence has the form:

This operation is denoted by the
symbol. To enter it into our calculator, one can use either ⊙ symbol or a function
.

The truth table of logical operation "exclusive not or" has the form:

It should be noted that the truth tables for
*binary*
logical operations "equivalence" and "exclusive or" are coincide. In case, the specified operations are
-ary, their
*truth tables* are differ. Note that the
-ary operations can only bе entered in our calculator as a corresponding functions, for example
, and the result of such expression will differ from the result of the expression
. Because the latter is interpreted as
, while in the case of
- the operation "equivalence" is performed immediately, taking into account all its arguments.

This operation is denoted by the
symbol. To enter it into our calculator, one can use either ⇒ symbol or => (equal sign, greater sign) construction.

The truth table of logical operation "implication" has the form:

When creating the truth table of a complex (composite) logical expression, it is necessary to use the truth tables of the corresponding logical operations given above.