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.
I'd throw in some order theory too. Posets, lattices, boolean algebras etc. All crop up pretty often, if you know how to recognise them.
In fact I think often when people recommend graph theory for computer science, they're thinking more about order theory (trees, DAGs, posets etc), or failing that, more the "basic algorithms over graphs" stuff than the "let's prove a bunch of clever theorems about k-colourings" kind of graph theory which you might get if you bought a book on it.
Although, gotta wonder how these stack-allocated objects interact with closures.