CALCULATE WITH CONFIDENCE

Set Theory & Logic

Argument Validity Calculator

Test propositional premises and a conclusion for semantic validity.

Set Theory & Logic

Enter values

Private calculation in your browser

Use the notation shown in each label and example. Inputs stay on this device and are never sent to a calculation service.

Result

—

Enter valid values to see the result.

Your entries are calculated in this browser and are not submitted to 365CALCS.COM.

Quick guide

How to use this calculator

  1. Enter values using the notation shown beside each field.
  2. Choose a calculation mode when the tool offers more than one interpretation.
  3. Read the primary answer first, then inspect the supporting details.

Calculation method

Apply the stated definition

No valuation may make every premise true and the conclusion false.

The calculator validates the mathematical domain before returning a result and does not replace undefined states with zero.

Worked example

Worked example

P->Q; P therefore Q is valid.

No valuation may make every premise true and the conclusion false.

Supported inputs

Precision and limits

Finite, bounded input

Set and logic tools use finite inputs so every result can be checked completely. Each page states its practical size limit.

Notation

Set elements are comma-separated text labels. Logic operators and relation-pair notation are documented in the relevant input labels.