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.
Rework Tautology and Contradiction without copying Logical classification. Begin with Logical expression and preserve the fixed condition. Predict the scale of the Tautology and Contradiction answer, then compare it with Logical classification. Store a changed the fixed condition as another Tautology and Contradiction case.
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.
All true means tautology, all false means contradiction, and a mixture means contingency.
Evaluate Logical expression as true and false in Tautology and Contradiction. Keep the result under the same Tautology and Contradiction parentheses and precedence.
Inspect the all-true and all-false Tautology and Contradiction rows. Check any implication boundary as a separate Tautology and Contradiction case.
Choose a nearby Logical expression whose effect on Logical classification is easy to anticipate. With the fixed condition held constant, the Tautology and Contradiction result should move in the expected direction. This controlled Tautology and Contradiction comparison is more revealing than several simultaneous edits.
Substitute the calculated Logical classification into the defining Tautology and Contradiction relationship when that reversal is possible. The recovered value should agree with Logical expression under the fixed condition. A mismatch points to rounding, entry order, or an assumption involving the fixed condition.
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.