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These argument forms involve complex propositions that are built up from simpler ones. When representing the arguments symbolically, we use lowercase letters to represent the simpler propositions.
Thanks to Aristotle and later logicians, the way deductions of different sorts work is well understood, and the various valid and invalid forms have been catalogued. But even among people who have not studied their works it is relatively rare to find sustained disagreement about whether an argument is valid. People are generally quite good at recognizing whether or not the premises follow necessarily from the conclusion.
That said, we do sometimes argue invalidly, particularly when we are not paying attention. Here are the three most common invalid argument forms (or “deductive fallacies”):
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