As a person who is absolutely terrible at explaining what is on their mind, naturally I love the idea of formal language. There aren't any double meanings that arise from subtle contextual differences, it stubbornly adheres to only one layer of context, which is that it means what it means. Novelists and poets, go eat your "lavished tomes of nuance and texture" (wow, count those double meanings!). So understanding formal language is the easy part most of the time, it's just like looking at an equation. The hard part is translating our imprecise natural language into formal language symbols. I'm still having difficulties with this, but generally when an English sentence uses "and", it means conjunction. "Or" could be inclusive or exclusive though (the "or" in this sentence is exclusive), but it is easy to tell the different between them. Inclusive or is disjunction, but exclusive or is more analogous to A "and not" B "or" B "and not" A. "And not" is also usually represented in English as "except", but the word "except" could translate into other symbols or operators depending on the context. One could say "and not" implies "except" but "except" does not imply "and not"!
Logical statements might have precise diction that I appreciate a lot, but their meaning and equivalent statements are a bit harder to internalize. For me, I don't really see why "antecedent implies consequent" could also be written as "(not antecedent) or (consequent)". de Morgan's law was more straightforward though, and I was able to see how that works with Venn diagrams, so maybe if I tried to draw a Venn diagram for any statement or rule I don't understand I would see the connection. Actually Venn diagrams help with vague English statements as well, so I might as well just draw them for everything. Actually truth tables would probably be better for most things. The point is to draw a diagram or use whatever tools you have at your disposal to help you understand.
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