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Here is para from wiki, about functional dependency in relation dbms

Given a relation R, a set of attributes X in R is said to functionally determine another set of attributes Y, also in R, (written X → Y) if, and only if, each X value is associated with precisely one Y value; R is then said to satisfy the functional dependency X → Y. Equivalently, the projection \pi_{X,Y}R is a function, i.e. Y is a function of X.[1][2] In simple words, if the values for the X attributes are known (say they are x), then the values for the Y attributes corresponding to x can be determined by looking them up in any tuple of R containing x. Customarily X is called the determinant set and Y the dependent set. A functional dependency FD: X → Y is called trivial if Y is a subset of X.

I could not get the last point "A functional dependency FD: X → Y is called trivial if Y is a subset of X."

please give me an example and explain it

Thank you :)
asked in Databases by Active (3.3k points)
edited by | 946 views

2 Answers

+3 votes
Best answer

The problem here is "trivial". A native English speaker wouldn't have any doubt in this. Here is one example usage of it:

(a) An engineering student having attended high school is trivial.

More details:

Now, coming to FD, we say 
X → Y when Y is dependent on X. That is, whenever X value changes Y value should change accordingly. Now consider X= {A,B,C} and Y = {A}, where Y is a subset of X. Let us consider a tuple of relation R containing X and Y (second one in the below table where x represents any value)


x x x x
first 456 chennai -
x x x x

Here, value of X for our tuple = {first, 456,chennai}, and value of Y = {first}. Now when "first" changes to say "second", it will change the value in both X as well as Y, as the attribute A is the same in both X and Y. So, there is no meaning in this FD as it is always there, and hence it becomes trivial. 

answered by Veteran (355k points)
selected by
+4 votes

For example if we consider {name, rollno} \rightarrow rollno.  here RHS is a subset of LHS , This type of dependency are called trivial

They are implicit.

answered by Boss (11.5k points)

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