please help me
why every all-key relation is in BCNF
for example if we have a relation:
ABC(A,B,C)
and this FD hold for ABC:
A->B
we have an all-key relation.
you know that A is a diterminant and not a candidate key
this relation doesn't satisfy BCNF conditions(I think!).

You really need to discuss this kind of problem with your teacher or your TA. You really need to understand the underlying principles instead of just getting the answer to the question or you'll be really lost as the class progresses.

-PatP

Your statement that "every all-key relation is in BCNF" is FALSE if "all-key" means that every attribute is a component of some candidate key.

Note also that if A->B then {A,B,C} is not a candidate key because it is reducible by removing the attribute B. Your example is not complete unless you tell us what the candidate keys are.

Like Pat, I recommend you first study the fundamentals before seeking help with your question.

Thank you.
I myself found out my answer.
An all-key relation is one whose only candidate (primary) key is constituted by all attributes of the relation.
This example shows a relation that really not an all-key relation, because there is an FD, A->B, so we can deduce : AC->B . We khow that AC->A and AC->C.
We can see that AC determines all of the attributes therefore is a candidate key.
By this condition we don't have an all-key relation, because ABC isn't the primary key.