This calculator creates a truth table for any logical expression. To get started, enter the boolean expression into the calculator.
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 tilde (~) symbol. 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.