Build a truth table for a logic expression with AND, OR, NOT, XOR, implication and equivalence, and classify it.
Classification
How to use this tool
For example: (A OR B) AND NOT C.
2 variables give 4 rows; 3 give 8.
Each row shows the inputs and the result.
Tautology, contradiction or contingency.
Formula & worked example
A AND B is true in 1 of 4 rows; A OR NOT A is a tautology.
Limitations — read this before you rely on it
Propositional logic only, up to 3 variables. It does not handle quantifiers, predicates or multi-valued logic.
Frequently asked questions
AND (&), OR (|), NOT (!), XOR (^), IMPLIES (>) and IFF (=), as words or symbols, plus brackets.
An expression true in every row, like A OR NOT A. A contradiction is false in every row; anything else is contingent.
2 to the power of the variable count: 4 rows for 2 variables, 8 for 3.
Yes: NOT first, then AND, XOR, OR, IMPLIES, IFF. Use brackets whenever the reading could be ambiguous.
Material implication: a false premise implies anything. Only true-premise-false-conclusion is false.