non trivial functional dependency in DBMS

Question

pls help me to find out non trivial functional dependency in a following table?

A.            B.              C
1             1               1
1             1               0
2             3               2
2             3               2

and also explain the basic concept behind it. thank you,,

Answer 1

A functional dependency answers the question, "Given one value for X, do I find one and only one value for Y?" Both X and Y are sets; each one represents one or more attributes.

So we can ask ourselves, "Given one value for 'A', do I find one and only one value for 'B'?" And the answer is "Yes". (Assuming the sample data is representative.) That leads to the nontrivial functional dependency A->B.

And we continue with the question, "Given one value for 'A', do I find one and only one value for 'C'?" And the answer is "No". Given 1 for 'A', we find two different values for 'C': 1 and 0. No functional dependency there.

Repeat for every possible combination of attributes.

Answer 2

Trivial: If an FD X → Y holds where Y subset of X, then it is called a trivial FD. Trivial FDs are always hold.

Non-trivial: If an FD X → Y holds where Y is not subset of X, then it is called non-trivial FD.

Completely non-trivial: If an FD X → Y holds where x intersect Y = Φ, is said to be completely non-trivial FD.

For example:

X = { b, c } and Y = { b, a }. If X → Y, then the FD is non-trivial but not completely non-trivial.