lossless join

Question

$R(X,Y,Z,W) is\  decomposed\  into \\ R_1(X,Y)\\ R_2(Y,Z)\\ R_3(Y,W).\\The\  FDs\  are\ :\\ X -> Y,\\ Z->Y,\\ Y->W \\ Find\ whether\ the\ decomposition\ is\ lossless\ or\ lossy\ ?$

Comments

it is lossy.

---

Lossy and FD preserving

---

R1&R3 will be combined ...but for R2

Let consider this example:-

X Y Z W

2  2  3  6

3  2  4  7

1 2   2   8  

 Now consider decomposition R2:-

Y  Z

2  3 

2  4

2   2  

R1R3=R'

X Y W

2  2  6

3  2  7

1 2   8  

now th3 natural join of R' and R2 wil give following relation:-

X Y Z W

9 touples...not like the old table

therefor

Lossy decomposition

---

Lossy and FD preservi

Answer 1

LOSSY

(X,Y) AND (Y.Z) HAS COMMON ATTRIBUTE Y WHICH IS NOT A PRIMARY KEY OF ANY OF THE TABLE(R1 OR R2).

Answer 2

lossy..