Valid argument in logic: meaning and examples

An argument is valid when its conclusion is true in every case where all its premises are true: no row of the truth table has every premise true and the conclusion false.

Validity is about form, not content. It says nothing about whether the premises are in fact true; it says that if they were, the conclusion could not fail. A valid argument with true premises is called sound. The test is a search for a counterexample, a row with all premises true and the conclusion false; if the search over every row finds none, the argument is valid, and if it finds one, that row is the refutation. Equivalently, the implication from the conjunction of the premises to the conclusion is a tautology.

The artefact on this page is modus ponens: premises A -> B and A, conclusion B. The 4-row table shows the premise columns true, true, false, true and false, false, true, true, and the conclusion column false, true, false, true. Only row 3, A = TRUE, B = TRUE, has both premises true, and there the conclusion is true too. The validity check holds, with the summary that no admissible assignment makes every premise true and the conclusion false, and the premise-consistency check holds with the witness A = TRUE, B = TRUE.

Validity is the central notion of a philosophy logic course and the property a rule reviewer checks when a policy is written as “from these facts, this follows”. The engine's argument mode exists for it: premises and a conclusion instead of named outputs. The term is confused with soundness (valid plus true premises), with the truth of the conclusion (a valid argument can have a false conclusion if a premise is false), and with vacuous validity, where the premises can never all be true.

Example

p1 — A -> B · premisep2 — A · premiseconclusion — B · conclusion

Exact checks

Does the conclusion follow from the premises? Yes · Exhaustively checked and solver cross-checked · 4 rows

Can all premises be true together? Yes Example assignment: A = T, B = T · Exhaustively checked and solver cross-checked · 4 rows

Truth table (4 rows)

Valid argument in logic: meaning and examples
#	A	B	p1	p2	conclusion
0	FALSE	FALSE	TRUE	FALSE	FALSE
1	FALSE	TRUE	TRUE	FALSE	TRUE
2	TRUE	FALSE	FALSE	TRUE	FALSE
3	TRUE	TRUE	TRUE	TRUE	TRUE

Plain-language reading

BeginnerConclusion: B is true.

IntermediateConclusion: B is true.

AdvancedConclusion: B is true.
Formal notation: B

The common slip

Judging an argument by whether its conclusion is true. An argument with a true conclusion can be invalid, as affirming the consequent shows, and a valid argument can have a false conclusion when a premise is false. Validity is about the rows, not about the world.

Questions

What does the engine do when the premises cannot all be true?

It still reports the argument valid, because there is no counterexample row, but it marks the verdict vacuous and the premise-consistency check reports that the premises are inconsistent. The glossary page on vacuous truth shows that case.

Guides

Valid vs sound arguments

Practice

Argument validity exercises with answers

Glossary

Generated from the Tangibool engine, semantics tangibool-semantics/1, engine 1.0.0, build 2026-11-07. Every table, map, simplification and verdict on these pages was computed by the Tangibool engine when the site was built, and every claim was re-checked by the same exact checker the app uses. Limits are stated where they apply. © 2026 Foreranger LTD.