A truth table lays out every possible combination of true/false values for a logical expression's variables and shows the resulting output for each one — the foundation of propositional logic, digital circuit design, and formal proofs. This calculator builds that table for any expression you type, using a safe, hand-written parser rather than a dynamic code-execution shortcut, and automatically classifies the result as a tautology, contradiction, or contingency.

How the calculator works

Your expression is read into a small parse tree that already encodes operator precedence: NOT binds tightest, then AND, then XOR, then OR, then IMPLIES, and finally IFF (the biconditional), which binds loosest — the same convention used in most logic textbooks. Every distinct single-letter variable is collected automatically, and the calculator generates all 2ⁿ possible true/false combinations for n variables, evaluating the parse tree once per row. No eval() or dynamic code execution is used anywhere — the parser only recognizes variables, the supported operators, and parentheses, so nothing you type can run as code.

Reading the input syntax

Variables must be single letters (A, B, C…), and operators can be typed three ways: as a keyword (AND, OR, NOT, XOR, IMPLIES or THEN, IFF), as an ASCII alias (&&, ||, !, ->, <->), or as the formal symbol (∧ ∨ ¬ ⊕ → ↔) — all three forms can be mixed freely in the same expression. Parentheses override the default precedence exactly like in arithmetic, so A OR (B AND NOT C) and (A OR B) AND NOT C produce different tables.

Limits and edge cases

The parser rejects anything that isn't a single-letter variable, a supported operator, or a parenthesis — multi-letter identifiers (like foo) throw a clear error rather than silently being ignored, since only single letters are treated as variables. To keep the table readable and the computation instant, expressions are capped at 8 distinct variables (256 rows) and 300 characters; going over either limit returns a plain-language error instead of a wrong or truncated table.