Classify a proposition as a tautology, contradiction, or contingency. Formula and logical classification remain visible in one place for independent verification.
A tautology is true on every assignment, a contradiction is false on every assignment, and a contingency has both outcomes.
In tautology and contradiction checker, the relationship among the quantities matters just as much as their arithmetic.
Generate the full truth column and test whether it contains all true, all false, or a mixture.
Classification checks proof claims, impossible conditions, always-on rules, and satisfiable specifications.
p|!p is a tautology, while p&!p is a contradiction. This Tautology and Contradiction Checker example can be compared with identity comparison.
A complex expression may look obvious but still need all assignments, especially when implication is nested.
An unexpected Tautology and Contradiction result usually points to field assignment or operand order before it points to the algorithm.
The input labels—logical expression—encode the model used on this page. Write Logical expression beside the source data when transferring this setup from paper or a spreadsheet. That step catches swapped roles and mismatched labels before they become a polished-looking Tautology and Contradiction result.
Negating a tautology produces a contradiction and vice versa. A one-field trial makes this relationship visible without reworking the entire example.
Choose how much of the Tautology and Contradiction structure to retain after considering how the result will be reused. Comparison may need only a few significant digits, while a later multi-step calculation benefits from carrying more. In either case, retain the page's formula with the logical classification so the underlying definition remains visible.
Logical equivalence can test whether an expression matches the constant true or false behavior. The distinction determines whether this page fits the original question.
If the result moves into a spreadsheet, give it a Tautology and Contradiction heading and retain Logical expression nearby. Context matters more than extra displayed digits.
All true means tautology, all false means contradiction, and a mixture means contingency.
A tautology is true on every assignment, a contradiction is false on every assignment, and a contingency has both outcomes.
Classification checks proof claims, impossible conditions, always-on rules, and satisfiable specifications.
A complex expression may look obvious but still need all assignments, especially when implication is nested.