1. Complete inference rules: FD: non-trivial
RHS is Single attr + non subset of LHS
proof: general and complete
disproof: one negative example is enough
Redefine key: set of attr functionally determine All other attrs and is “minimal” (no subset of key will be also key)
primary/super-/sub-key
binary relation: key? 1-1,1-m,m-m
Closure operator +: fundamental operator
Key: whose closure is all attr, and it is minimal
utility: check given FD and 3NF
why it works? Math. Proof. By induction
prove closure is a fixed point (try by yourself first, to be briefed next lecture)

2. Closure Utility: check given FD
diff forms of math induction: correct FD
1. no false positives: A1..An->B
2. no false negatives
FD’s augmentation (LHS) not RHS
Exercise: page /2/4
Data mining/Knowledge discovery from data(KDD): rule discovery-statistical support
FD discovery: find supporting for every tentative FD