https://maximummathematics.com/books/foundational-mathematics/logic/simplifying-logical-expressions/index.htmlIn the previous section we saw an example where we used tautologically true biconditionals to “simplify” complicated propositional expressions into simpler propositional expressions. Whatever we could say about the simpler expressions could also be said about their more complicated, logically equivalent counterparts (except perhaps our preference for working with the simpler expressions, of course). In this section we do more work with logical equivalencies, similar to what we saw in the examples seen previously. Our work here will bear a striking resemblance to our experience in dealing with the arithmetic and algebra of real numbers. In fact, the upcoming work we are about to engage with has been dubbed the “algebra of propositions.”Hugoen-US