1. Plan for Today Normal forms
Feedback from slides:
Explain 3nf/bcnf examples
Clarify dependency preservation
Kahoot: 4efa a2a58e5cf
Class worksheet – question 1
Lossless decompositions
Class worksheet – question 2
Dependency preserving decompositions

2. Question 1 Find a (minimal) key Z of R
For each nontrivial FD X⟶Y in F {
If X is not a superkey then {
For each A in Y\X {
If A is not in Z then return false }
Return true

3. state,city,street⟶zip, zip⟶state
Question 1 (cont’d)
If the algorithm returns true, then 3NF
The other direction is not necessarily true
state,city,street,zip
state,city,street⟶zip, zip⟶state
Z = {city , street , zip}

4. Question 1 (cont’d)
Find all (minimal) keys of R and let Z be the union
For each nontrivial FD X⟶Y in F {
If X is not a superkey then {
For each A in Y\X {
If A is not in Z then return false }
Return true

5. AB, BC, CD Question 2 (a) (A,B,C,D) A⟶B, B⟶C, D⟶A A B C D a1 a2 x13

6. AB, BC, CD Question 2 (a) (A,B,C,D) A⟶B, B⟶C, D⟶A A B C D a1 a2 a3 x14

7. AB, BC, CD Lossy! Question 2 (a) (A,B,C,D) A⟶B, B⟶C, D⟶A A B C D a1 a2
x14
x21
x24
x31
x32 a4
Lossy!

8. AB, BC, AD Question 2 (b) (A,B,C,D) A⟶B, B⟶C, D⟶A A B C D a1 a2 x13

9. AB, BC, AD Question 2 (b) (A,B,C,D) A⟶B, B⟶C, D⟶A A B C D a1 a2 x13

10. AB, BC, AD Lossless! Question 2 (b) (A,B,C,D) A⟶B, B⟶C, D⟶A A B C D a1
x13
x14
x21 a3
x24 a4
Lossless!