I just want to be sure... If i've two dependencies like
Will it be the same as this one
If I understand correctly your question, you are asking if the two sets of functional dependencies {a → c, b → c}
and {ab → c}
are equivalent. The answer to this question is no.
From either a → c
or b → c
you can prove ab → c
(by applying the definition of functional dependency: x → y
if and only if, when two tuples have the same values for x
, they have also the same values for y
). You can also derive ab → c
with the Armstrong’s Axioms (e.g. starting from a → c
and applying first the augmentation axiom with b
, obtaining ab → bc
, then applying the decomposition to obtain ab → c
).
But the viceversa is not true: you cannot prove from ab → c
that a → c
, neither that b → c
, and equivalently you cannot derive any of the two dependencies from ab → c
through the Armstrong’s Axioms. For an example, consider the dependency StudentNumber, CourseName → Grade
(that asserts that there can be only a Grade
from a certain couple StudentNumber
and CourseName
). From this dependency you cannot assert that for a StudentNumber
there is only a Grade
, or for a CourseName
there is only a Grade
.