To show that an argument is invalid you do not need symbols or truth tables. You need one counterexample: a situation in which all the premises are true and the conclusion is false. If such a situation is even possible, the structure does not guarantee the conclusion. There are two ways to find one. The first is to imagine a scenario for the original argument. For 'Some managers are engineers; some engineers are rude; so some managers are rude', picture a firm where the rude engineers happen not to be managers. The premises hold, the conclusion fails, so the argument is invalid. The second is to build a parallel argument with the same shape but obvious content: the pattern is 'some A are B; some B are C; so some A are C', and 'Some women are parents; some parents are men; so some women are men' exposes the leap at once. The parallel version is persuasive because nobody can defend its conclusion, yet it has exactly the same form. The method only proves invalidity; failing to find a counterexample is not proof of validity. After this Concept you can take an argument you suspect is invalid and construct a scenario or parallel argument with true premises and a false conclusion.
A counterexample is a simple way to prove an argument is invalid in logic. It is an argument with the same logical form as the original, but with true premises and a false conclusion. You use it when…