Understand the subject
What makes an argument valid?
An argument is valid when no valuation makes all premises true while its conclusion is false.
Use it to search directly for a counterexample to a propositional argument.
See the structure
What the rule checks
T T → TT F → FF T → TF F → T
valid ⇔ no true-premises / false-conclusion rowWorked interpretation
Read the result in context
P→Q and P therefore Q has no counterexample row.
Interpret with care
Important boundary
Validity concerns the form of the argument, not whether its premises are true in the real world.
Use the Set Operations Calculator to explore small finite examples.
Quick guide
How to use this calculator
- Enter values using the notation shown beside each field.
- Choose a calculation mode when the tool offers more than one interpretation.
- 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.
