3.1 Consider the STP example from the section THE PLACE OF DESIGN THEORY in Chapter 1. Give examples of the update anomalies that can arise with that example. Also give an appropriate decomposition, and show how that decomposition avoids those anomalies.

3.2 Nonloss decomposition is based on the idea that a relation can be decomposed into projections in such a way that the original relation can be recovered by joining those projections back together again. In fact, if projections r1 and r2 of relation r are such that every attribute of r is retained in at least one of r1 and r2, then joining r1 and r2 will always produce every tuple of r. Prove this assertion. (It follows from this fact that the problem with a decomposition that’s not nonloss isn’t that the join loses tuples—rather, it’s that it produces additional, or “spurious,” tuples. Since we have no way in general of knowing which if any of the tuples in the join are spurious and which are genuine, the decomposition has lost information.)

3.3 NORMALIZATION SERVES TWO PURPOSES. Explain this remark in your own words. Do you think the point is widely understood?