Click "Generate Formula" to start!
Complete the truth table to understand satisfiability and validity of propositional formulas.
• Generate a random propositional logic formula
• Fill out the truth table by clicking on the empty cells
• Determine if the formula is satisfiable or unsatisfiable
• A formula is satisfiable if at least one row evaluates to True
• ∧ (AND): True only when both operands are True
• ∨ (OR): False only when both operands are False
• ¬ (NOT): Negates the truth value
• → (IMPLIES): False only when antecedent is True and consequent is False
• Satisfiable: At least one assignment makes the formula True
• Unsatisfiable: No assignment makes the formula True
• Valid: All assignments make the formula True
• Invalid: At least one assignment makes the formula False
A propositional formula is:
Examples:
Truth tables systematically list all possible truth value assignments:
Logical Operators:
| T | T | T |
| T | F | F |
| F | T | F |
| F | F | F |
| T | T | T |
| T | F | T |
| F | T | T |
| F | F | F |