How to Make an Introductory Class in Set Theory and Logic Exciting I am teaching a "proof techniques" class for sophomore math majors.  We start out defining sets and what you can do with them (intersection, union, cartesian product, etc.).  We then move on to predicate logic and simple proofs using the rules of first order logic.  After that we prove simple math statements via direct proof, contrapositive, contradiction, induction, etc. Finally, we end with basic, but important concepts, injective/surjective, cardinality, modular arithmetic, and relations.
I am having a hard time keeping the class interested in the beginning set theory and logic part of the course.  It is pretty dry material.  What types of games or group activities might be both more enjoyable than my lectures and instructive?

Can I echo @dfeur's suggestion that a bit of history and conceptual commentary could be intriguing/fun/motivational (at least for more intellectually curious students)? 
Sets How did sets get into the story in the nineteenth century (the arithmetization of analysis)? Frege's disaster and Russell's paradox. Zermelo's response. The idea of the cumulative hierarchy and other conceptions of the universe of sets. Why such a simple claim as the Continuum Hypothesis remains problematic.
Logic Something about how/why classical first-order logic becomes standard. Why constuctivists balk at excluded middle. Why it is so difficult to do better than the material conditional to regiment indicative conditionals. The motivation for Frege's quantifier/variable regimentation of general propositions. The conceptual motivations behind different approaches to logic (axiomatic, natural deduction). Whether some mathematical reasoning is not first-order.
It's good for students to see e.g. that while (versions of) first-order logic as a theory are of course cleanly definable, it isn't so cut and dried why we've come to treat FOL as canonical. And as @Asaf says, if you find [some of] these questions intriguing, then your puzzlement and interest in them should be infectious.
