Normalisation

Question

A functional dependency X->y is trivial if y⊆x right ??

Answer 1

Yes. Actually this shouldn't be a question if one understands the meaning of "trivial". Trivial basically means "the question has no need". One example of a trivial property is:

• Do human beings have brain?

There is no need to answer this question as it is trivially true- because all human beings have brain. 

Now a non-trivial property would be 

• Do human beings have intelligence?

Now, this need not be true for all human beings and hence non-trivial. 

 

Now, coming to functional dependency we say A- > B, when the same A element always causes the same B element. i.e., whenever A element repeats B element also repeats. If A is a composite set (x,y) coming from attributes X and Y and B is the attribute Y (hence B ⊂ A), we are sure than whenever the A element repeats the B element also repeats. That is, the functional dependency cannot be violated whatever be the elements - hence TRIVIAL. 

Comments

@Arjun sir at the last line of your ans you meant to say FD will not be violated for any instances of of the attributes involving? means say address is a composite attribute having atomic attribute street and pin.. so pin will always repeat for the particular address no matter in  how many tuples it is repeated in the relation..? hence address->pin is trivial fd as pin is already a constituting attribute i.e proper subset attribute of address?Pls clear sir..

Answer 2

ya..  functional dependency X->y is trivial if y⊆x..