database normalization - Decomposition into ABC & CDE and preserving functional dependencies -

consider relation r 5 attributes abcde. assume r decomposed 2 smaller relations abc , cde. define s relation (abc naturaljoin cde). a) assume above decomposition lossless join. dependency guarantees lossless join property. b) give additional fd such “dependency preserving” property violated decomposition. c) give 2 additional fd's preserved decomposition.

question seems different me because there no fd given , asking:

a)

r1=(a,b,c) r2=(c,d,e) r1∩r2 =c (how can control dependency now)  f1' = {a->b,a->c,b->c,b->a,c->a,c->b,ab->c,ac->b,bc->a...}  f2' = {c->d,c->e,d->e....} 

then find f' ??

b,c) how check , need possible fd's r1 , r2

the question assuming things hasn't said clearly. abcde subject jd *{abc,cde} while not being subject nontrivial fds @ all.

but suppose relation subject fds , isn't subject jds other ones imply. if c ck join lossless. c -> abcde holds, because ck determines attributes, , c -> abde holds, because ck determines other attributes. no other fd holding imply join lossless, although requires tedium (by looking @ every possible case of ck) or inspiration show.

both these fds guarantee losslessness. although if 1 of these holds other holds, , express same condition. question sloppy. or question might consider 2 expressions express same fd in sense of condition, fd expression , not condition, sloppy.

i suspect questioner wanted give fd holding guarantee losslessness. rid of complications.