Logical Validity Calculator

Test premises against conclusions with truth tables. Compare every row before trusting any final argument. Build stronger reasoning using clear logical evidence every time.

Calculator

NOT: !, ~, ¬, NOT

AND: &, ∧, AND

OR: |, ∨, OR

XOR: ^, XOR

IMPLIES: ->, =>, →

IFF: <->, <=>, ↔

Example data table

Argument form Premises Conclusion Expected result
Modus ponens P -> Q; P Q Valid
Modus tollens P -> Q; !Q !P Valid
Affirming the consequent P -> Q; Q P Invalid
Disjunctive syllogism P | Q; !P Q Valid

Formula used

An argument is valid when every valuation that makes all premises true also makes the conclusion true.

Validity test: Valid ⇔ no v exists where P1 ∧ P2 ∧ ... ∧ Pn is true and C is false.

Equivalent tautology: (P1 ∧ P2 ∧ ... ∧ Pn) → C must be true on every truth-table row.

Counterexample test: Counterexample ⇔ all premises are true and the conclusion is false.

How to use this calculator

  1. Enter each premise on a separate line.
  2. Enter the conclusion in the conclusion box.
  3. Use the operator guide for symbols and text operators.
  4. Choose row display, truth labels, and variable order.
  5. Press the submit button to see validity results above the form.
  6. Download the CSV or PDF file when you need a saved report.

About the Logical Validity Calculator

A logical validity calculator checks whether a conclusion must be true whenever all premises are true. It does not judge style, emotion, or real world facts. It studies argument form. This tool builds a complete truth table for every variable found in your statements. It then tests each row. If any row makes all premises true and the conclusion false, the argument is invalid. That row is a counterexample. If no such row exists, the argument is valid.

Why validity matters

Validity is useful in debate, math, programming, law, and everyday planning. It helps separate good structure from persuasive wording. A statement can sound confident and still fail logically. Another statement can look simple and remain valid. Truth tables give a visible method. They list every possible true or false assignment. This removes guesswork. It also helps students learn connectives such as conjunction, disjunction, negation, implication, and biconditional.

Input options

Use one premise per line. Enter the conclusion in its own field. You may use letters like P, Q, and R. You may also use longer names such as Rain, WetRoad, or Alarm. Choose symbols from the guide. The parser accepts common text and symbol operators. You can compare premises using AND, OR, NOT, XOR, implication, and equivalence. Parentheses are supported. They are important when a statement has several operators.

Reading the answer

The result area appears above the form after calculation. It shows validity status, variables, total rows, rows where all premises are true, and counterexamples. A valid argument has no counterexample. An invalid argument includes at least one row that proves failure. The CSV button exports the truth table for spreadsheets. The PDF button saves a clean summary and table view.

Practical tips

Start with small formulas. Check operator spelling. Add parentheses when meaning could be unclear. Review counterexamples carefully. They often reveal the exact weakness in an argument. Use the example table to learn patterns before testing longer cases.

For advanced study, test classic forms such as modus ponens, modus tollens, hypothetical syllogism, and affirming the consequent. Compare valid and invalid forms side by side. The differences become clear when each row is displayed. Save results to document your reasoning practice later.

FAQs

What is logical validity?

Logical validity means the conclusion cannot be false when all premises are true. It depends on structure, not on whether the premises are actually true in the real world.

What is a counterexample?

A counterexample is one truth-table row where every premise is true and the conclusion is false. One counterexample is enough to prove invalidity.

Can I use words instead of symbols?

Yes. You can use words such as AND, OR, NOT, and XOR. You can also use symbols like &, |, !, ->, and <->.

Why are parentheses important?

Parentheses show the intended grouping. They prevent confusion when a formula contains several operators with different precedence levels.

What does vacuous validity mean?

Vacuous validity occurs when premises cannot all be true together. The argument has no counterexample, but the premise set is inconsistent.

How many variables can I test?

You can choose limits of 6, 8, or 10 variables. Higher limits create larger truth tables, so they may take longer to display.

Does validity mean the conclusion is true?

No. Validity means the conclusion follows from the premises. The conclusion may still be false if one or more premises are false.

What does the CSV file include?

The CSV file includes variable assignments, premise values, conclusion values, all-premise status, and counterexample labels for every truth-table row.

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