self doubt

Question

relation schema with no non trivial fd's then relation is always in bcnf.

please someone explain this i am not able to get it.

Comments

if there is no non trivial functional dependecy, it means there are all trivial functional dependency.

the above line simply means there is actually no functional dependecy, because trivial functional dependecies are implicit.

now if there is no functional dependency, then it is definately in BCNF because nothing wil voilate it to be in BCNF

PS: candidate key for it will be all the attributes taken all at a time.

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thank u

i got it

Answer 1

If a functional dependency X->Y holds true where Y is not a subset of X then this dependency is called non trivial Functional dependency

so with no non trivial dependency we will have only trivial dependencies such  as A->A or A-> phi..

so for BCNF we need A->B where A is a superkey so we will have the whole table as a Primary key and no partial or transitive dependencies will be there because we have no non trivial dependencies.

Answer 2

bcnf means for every x->y present in fd set  x must be sk or ck........

and no non trivial fd means there is trivial fd so for every x->y x is superset of yand hence is bcnf ...and for more just frame a example using needed conditions ..