In formal logic, sentences and arguments in English are translated into mathematical languages with well-defined properties. If all goes well, properties of the argument that were hard to discern become clearer. This book covers translation, formal semantics, and proof theory for both sentential logic and quantified logic. Each chapter contains practice exercises; solutions to selected exercises appear in an appendix.
Logic and Foundations of Mathematics
Magnus, P.D., "Forall x: An introduction to formal logic" (2014). Philosophy Faculty Books. 3.