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What is Truth Table Generator?

Enter a logical expression and get a complete truth table showing every combination of input values and the resulting output. The generator supports AND, OR, NOT, XOR, implication, and biconditional operators, making it a practical tool for discrete math, digital logic design, and philosophical logic coursework.

How to Use

  1. 1Enter a logical expression using variable names (p, q, r, etc.)
  2. 2Use standard operators: AND (∧ or &), OR (∨ or |), NOT (¬ or !), XOR (⊕), IMPLIES (→ or =>), BICONDITIONAL (↔ or <=>)
  3. 3Click Generate to produce the truth table
  4. 4Review intermediate columns to trace sub-expression evaluation
  5. 5Copy the table for use in assignments or documentation

Key Features

  • Support for AND, OR, NOT, XOR, implication, biconditional
  • Automatic variable detection
  • Intermediate sub-expression columns
  • Up to 8 variables (256 rows)
  • Tautology and contradiction detection
  • Copy table to clipboard
  • Multiple notation styles accepted (symbolic and text)

Common Use Cases

  • Discrete mathematics

    Verify logical equivalences and tautologies for proofs and assignments.

  • Digital circuit design

    Map Boolean functions to truth tables before implementing them in hardware.

  • Programming logic

    Test complex conditional expressions to make sure they cover all edge cases.

  • Philosophy coursework

    Evaluate argument validity by constructing truth tables for premises and conclusions.

Examples

  • De Morgan's Law

    Enter ¬(p ∧ q) and (¬p ∨ ¬q) separately, then compare their truth table columns — they will match.

  • Implication check

    Enter p → q to see that implication is only false when p is true and q is false.

The Details

The generator parses propositional logic expressions, identifies all unique variables, and systematically enumerates every possible truth-value assignment. Intermediate columns show the result of each sub-expression, so you can trace how the final value is derived step by step. This is especially helpful when debugging complex Boolean expressions or verifying logical equivalences.

Frequently Asked Questions

How many variables can I use?

Up to 8. Each additional variable doubles the number of rows, so 8 variables produce 256 rows.

What operator symbols are accepted?

You can use symbolic notation (∧, ∨, ¬, →, ↔) or programmer-friendly alternatives (&, |, !, =>, <=>).

Does it simplify expressions?

The generator evaluates expressions but does not simplify them. Use the output to manually identify simplification opportunities.

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All processing happens directly in your browser. Your files never leave your device and are never uploaded to any server.