Now that we know about sets, we can construct some new ones from old ones in even more ways than we did before. In this section we look closely at two special sets: the first is called the power set, and the second is called the Cartesian product of two sets. The power set introduces a new level of thought about notation, and the solved exercises and examples aim to deal with any confusion that might arise. The chapter concludes with a discussion of relations on sets, setting the stage for Chapter 10. In Tips on Writing we point out some common mistakes in mathematical writing, and we encourage the students to make their solutions not only clear, but also concise. Specific suggestions are included.