Truth Table Generator

AND, OR, and XOR are all associative operations, meaning it makes no difference to the final truth value whether you group the variables from the left or the right — the answer comes out the same either way. NAND is commutative but not associative: (A NAND B) NAND C and A NAND (B NAND C) can disagree on the same inputs, so like IMPLIES it needs a fixed grouping — the calculator just happens to evaluate it left-to-right, the same direction as AND, OR, and XOR. Material implication is the operation evaluated in the opposite direction: A implies (B implies C) and (A implies B) implies C can also disagree on the same inputs, so the calculator has to commit to one grouping there too, and it follows the standard mathematical convention of evaluating IMPLIES from the right.

Number of Variables is rounded to the nearest whole number before the calculator builds any rows, and a small percentage nudge on a value as low as 2 isn't large enough to round up to 3. The variable count absolutely does matter — moving it from 2 to 3 doubles the total number of rows outright — it just isn't visible to a wiggle this small.

It counts outcomes rather than reasoning symbolically: Tautology is reported when every single one of the 2ⁿ evaluated rows comes out true, and Contradiction is reported when every row comes out false. Anything in between — some rows true, some false — is neither, even if the formula has some deeper structural property a symbolic proof method might flag.

It's simply the count of rows that evaluated to true, divided by the total row count (2ⁿ for n variables), expressed as a percentage. For iterated XOR (parity), that percentage lands at exactly 50% for any number of variables in the 2 to 4 range this calculator supports, not just an even count, while AND across several variables produces a much smaller share of true rows, since every single variable has to be true simultaneously.