Validity and Counterexamples

An argument is valid when there is no possible assignment in which every premise is true while the conclusion is false.

This definition is about the relationship between premises and conclusion. It does not require every premise to be a tautology, and it does not say that a valid conclusion must be true under every unrelated assignment.

When a proposed argument is invalid, one counterexample row proves the point: all premises are true on that row, but the conclusion is false. The most useful validity table therefore highlights the relevant rows instead of treating every row as equally important.

Open the Argument mode inside the Truth Table lab to build original arguments and inspect counterexamples.