What operators are supported?

AND (also & or &&), OR (also | or ||), NOT (also ! or ~), XOR (also ^), NAND, NOR, implication (-> or =>), and biconditional ( or ). You can mix keyword and symbol forms freely.

How many variables can I use?

Up to 6 variables, which produces a table of 64 rows. Beyond 6, tables become impractically large to read, so the calculator shows an error instead.

A tautology is an expression that evaluates to true for every possible combination of its variables — for example, 'A OR NOT A' is always true, no matter what A is.

What is a contradiction?

A contradiction is an expression that evaluates to false for every possible combination — for example, 'A AND NOT A' can never be true.

What's the difference between implication and biconditional?

Implication (A -> B) is false only when A is true and B is false — it means 'if A then B'. Biconditional (A B) is true only when A and B have the same value — it means 'A if and only if B'.

How do parentheses affect the order of operations?

Without parentheses, NOT is evaluated first, then AND/NAND, then XOR, then OR/NOR, then implication, then biconditional (in that order, matching standard logic convention). Parentheses override this and force a specific grouping to be evaluated first.

What's the difference between NAND/NOR and AND/OR?

NAND is the negation of AND (true unless both inputs are true), and NOR is the negation of OR (true only when both inputs are false). They're the basis of NAND/NOR logic gate design, since either gate alone can build any other logic function.

Can I use lowercase variable names?

Yes, variable names are case-sensitive as identifiers but keywords like AND/OR/NOT are recognized regardless of case, so 'and' and 'AND' behave identically as operators.

Truth Table Generator — Evaluate Any Boolean Expression

Our Truth Table Generator parses any boolean expression you type — using variables like A, B, C and operators AND, OR, NOT, XOR, NAND, NOR, implication (->), and biconditional (<->) — and evaluates it across every possible combination of true/false inputs, up to 6 variables. The result is a complete, correctly ordered truth table, with automatic detection of whether your expression is a tautology (always true), a contradiction (always false), or a genuine contingency.

Quick Answer

Type a boolean expression using variables and operators (AND, OR, NOT, XOR, NAND, NOR, ->, <->), and this generator evaluates it across every true/false combination of your variables (up to 6), producing a complete truth table and flagging tautologies or contradictions automatically.

Boolean expression

Supports AND, OR, NOT, XOR, NAND, NOR, -> (implies), <-> (iff), and parentheses.

How to Use the Truth Table Generator — Boolean Logic Expressions Online

1
Type a boolean expression using variables (A, B, C, ...) and operators like AND, OR, NOT, XOR, NAND, NOR, ->, and <->.
2
Use parentheses to control the order of evaluation, just like in algebra.
3
Click 'Generate' to build the full truth table for every combination of your variables.
4
Check the tautology/contradiction banner to instantly see if your expression is always true or always false.

Why Use Truth Table Generator — Boolean Logic Expressions Online?

Truth tables are the definitive way to verify a boolean expression's behavior — unlike simplifying by hand, a truth table can't hide a subtle logic error, because it checks literally every possible input combination. This is essential for digital logic design, programming conditional statements correctly, and formal logic coursework. Our generator supports the full standard operator set, including the conditional (implication) and biconditional operators that many simpler tools skip, and automatically flags tautologies and contradictions, which are exactly the patterns that indicate a redundant or broken condition in real code.

Frequently Asked Questions

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