CS348 Lecture : Assignment #2 - Solution Fall 2009

• School: University of Waterloo
• Department: Computer Science
• Course: CS348
• Professor: Ihab Ilyas

Document Summary

Z is a subset of y so we have: y z. X y and y z (transitivity) x z. X z and z w (transitivity) x w. Using b1 and b2, we have (y y) implies that (yz y). We thus conclude that y x implies that x y. We thus conclude that x y implies that xz yz. Then from b3, we get x z (by assuming. We thus conclude that x y, y z implies that x z. Proving b1: since x x, we get from reflexivity that x x, which proves b1. Then, by transitivity we have xz y, which proves b2. By augmentation we get xw zw, which proves b3. We compute the closure of b as follows: We conclude that b is a super key. Since b is minimal so it is also a candidate key. Using s nc: {s,p,n,c,x,y,q} is split to {s,p,x,y,q} and {s,n,c}