Logical Statement Evaluator Calculator

Analyze statements with variables, operators, and truth tables. Check tautologies, contingencies, equivalence, and argument validity. See every logical outcome with structured results and charts.

Enter Your Logic Setup

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Supported operators

NOT or !, AND or &, OR or |, XOR or ^.

Use -> for implication and <-> for equivalence.

NAND and NOR are also supported.

Example inputs

Expression: (P AND Q) -> R

Equivalence: P -> Q and (NOT P) OR Q

Assignments: P=1, Q=0, R=1

Example Data Table

Example Statement Interpretation Expected Result
1 P OR NOT P Law of excluded middle Tautology
2 P AND NOT P Direct contradiction Contradiction
3 P -> Q Conditional relation Contingency
4 (P -> Q) <-> ((NOT P) OR Q) Implication equivalence rule Equivalent
5 P -> Q, Q -> R, P therefore R Hypothetical syllogism chain Valid argument

Formula Used

This calculator follows Boolean algebra and propositional logic rules. Each row assigns truth values to variables and then evaluates operators by precedence.

  • NOT P = true only when P is false.
  • P AND Q = true only when both operands are true.
  • P OR Q = true when at least one operand is true.
  • P XOR Q = true when exactly one operand is true.
  • P -> Q = NOT P OR Q.
  • P <-> Q = true when both sides share the same truth value.
  • P NAND Q = NOT (P AND Q).
  • P NOR Q = NOT (P OR Q).

How to Use This Calculator

  1. Choose the evaluation mode that matches your logic task.
  2. Enter the main expression using variables like P, Q, and R.
  3. Add a second expression for equivalence mode when needed.
  4. Enter one premise per line and a conclusion for argument checks.
  5. Provide assignments like P=1, Q=0 for specific evaluation.
  6. Set a variable order if you want custom truth table columns.
  7. Click the button to generate results, truth rows, and the chart.
  8. Use CSV or PDF export after the table appears.

FAQs

1. What does this calculator evaluate?

It evaluates propositional logic statements, builds truth tables, checks equivalence, and tests whether premises logically support a conclusion.

2. Which operators can I enter?

You can use NOT, AND, OR, XOR, NAND, NOR, implication, and equivalence. Symbol forms like !, &, |, ^, ->, and <-> also work.

3. What is a tautology?

A tautology is a statement that stays true for every possible assignment of its variables. The calculator labels it automatically after evaluation.

4. What is a contradiction?

A contradiction is a statement that becomes false for every possible variable assignment. It never produces a true row in the truth table.

5. How does equivalence checking work?

The calculator compares both expressions row by row. If every row matches, the expressions are logically equivalent.

6. What makes an argument valid here?

An argument is valid when no truth table row makes all premises true and the conclusion false. Any such row is a counterexample.

7. Why is there a row limit?

Truth tables grow exponentially with more variables. A row limit keeps the page fast, readable, and practical for regular study use.

8. Can I export my results?

Yes. After evaluation, you can download the current table as a CSV file or a PDF report for sharing, printing, or revision.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.