When it comes to first-order logic, you don't actually need this to reason about conditionals. That's just Propositional Logic (or Boolean Algebra, if you want

When it comes to first-order logic, you don't actually need this to reason about conditionals. That's just Propositional Logic (or Boolean Algebra, if you want to put it in a slightly more abstract setting, which wouldn't hurt since you can then apply it to other related things like set union/intersection/complement). First-order logic is really useful for Relational Algebra though. Which you should know if you do anything with relational databases.