Understanding the Calculator
Discrete mathematics uses logic to test whether statements are sound. This calculator turns symbolic propositions into a complete truth table. It also checks tautologies, contradictions, contingencies, equivalence, and implication. You can use it for homework, tutoring, proofs, software rules, and digital circuit ideas.
Why Logic Tables Matter
A truth table lists every possible truth assignment for the variables in a proposition. Each row shows one case. The final column shows whether the statement is true or false under that case. This makes hidden patterns visible. It also prevents guessing. When every row is true, the formula is a tautology. When every row is false, it is a contradiction. Mixed results mean the formula is a contingency.
Advanced Logic Checks
Advanced logic work often compares two formulas. Two formulas are equivalent when they match in every row. An implication is valid when no row makes the premise true and the conclusion false. This calculator checks both conditions. It also creates disjunctive and conjunctive normal forms when the variable count is practical. These forms help with proof writing, switching algebra, and simplification.
Input Syntax
Enter variables with letters such as p, q, and r. Use NOT, AND, OR, XOR, NAND, NOR, implication, and biconditional operators. Parentheses help control order. The calculator uses standard precedence, so negation is handled first. Conjunction follows. Then exclusive logic and disjunction are evaluated. Implication and biconditional checks are handled last.
Export and Review
The result area appears before the form after calculation. This keeps the answer easy to find. You can export the current truth table as a CSV file for spreadsheets. You can also save a PDF for sharing, printing, or class notes. The example table gives ready formulas to test. It is useful when you want to learn the accepted syntax quickly.
Study Benefit
This tool is meant for careful reasoning, not only quick answers. Review the classification summary first. Then scan the counterexample rows if a rule fails. Finally, compare the generated normal forms with your class method. That routine builds strong logic habits and reduces mistakes in discrete mathematics.
Because every row is produced directly from the operators, the work stays transparent. You can copy the table into reports, compare manual answers, and find the exact assignment that breaks a proposed theorem before final submission or review.