https://maximummathematics.com/books/foundational-mathematics/proof/rules-of-inference/index.htmlWe’ve already seen that, with ever-larger numbers of component propositions, a truth table requires more and more rows to complete — and that logical equivalencies let us simplify compound propositions without needing a truth table at all. We can bypass truth tables when determining whether an argument is valid too. Instead of logical equivalencies, though, we use logical implications. In this section, we collect a list of commonly occurring logical implications, and see how to use them strategically. We’ll still verify each one with a truth table — the point here is just to build up a list of implications we can use later.Hugoen-US