Logic Proof Calculator

Logic Proof Truth Table Generator

This calculator generates a truth table for a given logical expression, helping you verify its validity, identify tautologies, contradictions, or contingencies.

Use variables P, Q, R. Operators: NOT, AND, OR. Use parentheses for grouping. Example: (P AND Q) OR (NOT R)

function calculateTruthTable() { var expression = document.getElementById("logicalExpression").value.trim().toUpperCase(); var resultDiv = document.getElementById("truthTableResult"); resultDiv.innerHTML = ""; // Clear previous results if (!expression) { resultDiv.innerHTML = "Please enter a logical expression."; return; } // Identify variables present in the expression var variables = []; if (expression.includes("P")) variables.push("P"); if (expression.includes("Q")) variables.push("Q"); if (expression.includes("R")) variables.push("R"); if (variables.length === 0) { resultDiv.innerHTML = "No propositional variables (P, Q, R) found in the expression. Please use P, Q, or R."; return; } // Prepare the expression for JavaScript eval() // Replace logical operators with JS equivalents var jsExpression = expression; jsExpression = jsExpression.replace(/NOT/g, "!"); jsExpression = jsExpression.replace(/AND/g, "&&"); jsExpression = jsExpression.replace(/OR/g, "||"); // Build the truth table HTML var tableHTML = ""; // Add variable headers for (var i = 0; i < variables.length; i++) { tableHTML += ""; } // Add expression header tableHTML += ""; var numRows = Math.pow(2, variables.length); var isTautology = true; var isContradiction = true; for (var i = 0; i < numRows; i++) { tableHTML += ""; var currentEvalExpression = jsExpression; var varValues = {}; // Store current truth values for P, Q, R // Assign truth values based on binary representation of i for (var j = 0; j > (variables.length – 1 – j)) & 1) === 1; // true or false varValues[variables[j]] = value; tableHTML += ""; // Replace variables in the expression string for eval // Use a regex with word boundary to avoid replacing parts of other words currentEvalExpression = currentEvalExpression.replace(new RegExp("\\b" + variables[j] + "\\b", "g"), value); } var result; try { result = eval(currentEvalExpression); if (typeof result !== 'boolean') { throw new Error("Expression did not evaluate to a boolean. Check for syntax errors or unsupported operators."); } } catch (e) { resultDiv.innerHTML = "Error evaluating expression: " + e.message + ". Please check your syntax."; return; } tableHTML += ""; tableHTML += ""; if (result === false) { isTautology = false; } if (result === true) { isContradiction = false; } } tableHTML += "

" + variables[i] + "	" + expression + "
" + (value ? "T" : "F") + "	" + (result ? "T" : "F") + "

"; resultDiv.innerHTML = tableHTML; var conclusion = ""; if (isTautology) { conclusion = "The expression is a Tautology (always true)."; } else if (isContradiction) { conclusion = "The expression is a Contradiction (always false)."; } else { conclusion = "The expression is a Contingency (can be true or false)."; } resultDiv.innerHTML += conclusion; }

Understanding the Logic Proof Truth Table Generator

A logic proof calculator, specifically a truth table generator, is an essential tool in propositional logic. It helps you systematically determine the truth value of a complex logical expression for every possible combination of truth values of its constituent simple propositions.

What is a Truth Table?

A truth table is a mathematical table used in logic to compute the functional values of logical expressions. It lists all possible truth values (True or False) for the propositional variables involved and shows the resulting truth value of the entire expression for each combination.

Why Use a Truth Table Generator?

• Verify Validity: Determine if a logical argument is valid by checking if the conclusion is true whenever all premises are true.
• Identify Tautologies: An expression that is always true, regardless of the truth values of its variables (e.g., P OR NOT P).
• Identify Contradictions: An expression that is always false, regardless of the truth values of its variables (e.g., P AND NOT P).
• Identify Contingencies: An expression that can be true or false depending on the truth values of its variables.
• Understand Logical Equivalence: Compare two expressions to see if they have identical truth tables, meaning they are logically equivalent.

How to Use This Calculator

Our Logic Proof Truth Table Generator is designed for simplicity and clarity. Follow these steps:

1. Enter Your Expression: In the "Logical Expression" input field, type your logical statement.
2. Use Standard Variables: The calculator supports propositional variables P, Q, and R.
3. Use Supported Operators:
   • NOT (Negation): Reverses the truth value.
   • AND (Conjunction): True only if both operands are true.
   • OR (Disjunction): True if at least one operand is true.
4. Use Parentheses: Always use parentheses () to group parts of your expression and ensure the correct order of operations. For example, (P AND Q) OR R is different from P AND (Q OR R).
5. Click "Generate Truth Table": The calculator will process your input and display a detailed truth table below.

Examples of Logical Expressions:

• Simple Conjunction: P AND Q

  This expression is true only when both P and Q are true.

• Disjunction with Negation: P OR (NOT Q)

  This expression is true if P is true, or if Q is false (or both).

• Complex Expression: (P AND Q) OR (NOT R)

  This expression is true if both P and Q are true, OR if R is false.

• Tautology Example: P OR (NOT P)

  This expression will always evaluate to true.

• Contradiction Example: P AND (NOT P)

  This expression will always evaluate to false.

By using this tool, you can quickly and accurately analyze logical statements, making your study of logic more efficient and understandable.