I teach the introductory logic course in the philosophy PhD program at CUNY on a regular basis. Here is the course description:

PHIL 72000 – Logic

This course is a philosophical introduction to classical symbolic logic. No prior background in logic is assumed. We will study sentential logic and first-order predicate logic with identity. Topics to be covered include semantics, syntax, and proof procedures. We will also cover the metalogical concepts of soundness and completeness. Along the way, we will take a look at some central problems in the philosophy of logic, motivations for non-classical logics, and the relevance of logic to other areas of philosophy — in particular philosophy of language and metaphysics. The goal is to achieve both a practical mastery and philosophical understanding of elementary logic.

One of two textbooks for the course is Greg Restall’s Logic (2006). The book was published simultaneously by McGill-Queen’s University Press (978-0-773524231) and Routledge (978-0-415400688).  It is available online from the publishers: McGill-Queen’s: <http://www.mqup.ca>; Routledge: <www.routledge.com>. It is also available as an ebook in the Graduate Center library.

We use Virginia Klenk’s Understanding Symbolic Logic (4th or 5th edition) as a workbook. You can find used copies on Amazon or Abe Books.

I supplement these texts with lecture notes and handouts.

A one-hour problems session and tutorial is held after each class. Attendance is optional.