Trivial and Non Trivial Functional Dependency examples

Trivial and Non Trivial Functional Dependency examples –

Trivial Functional Dependency – 

Some functional dependencies are said to be trivial because they are satisfied by all relations. Functional dependency of the form A–>B is trivial if B subset= A . or
A trivial Functional Dependency is the one where RHS is a subset of LHS.

Example, A-->A is satisfied  by all relations involving attribute A.
SSN-->SSN
PNUMBER-->PNUMBER
SSN PNUMBER -->PNUMBER
SSN PNUMBER --> SSN PNUMBER

Non Trivial Functional Dependency – 

Non Trivial Functional Dependency can be categorized into –

  • Complete Non Trivial Functional Dependency
  • Semi Non Trivial Functional Dependency

Complete Non Trivial Functional Dependency – A Functional Dependency is completely non trivial if none of the RHS attributes are part of the LHS attributes.

Example, SSN --> Ename,
PNUMBER --> PNAME
PNUMBER--> BDATE    X

Semi Non Trivial Functional Dependencies – A Functional Dependency is semi non trivial if atleast one of the RHS attributes are not part of the LHS attributes.

{TRIVIAL + NONTRIVIAL}

Question 1 :
A B C
1 1 1
1 2 1
2 1 2
2 2 3 
Identify Non Trivial Functional Dependency ?
Solution :
S.NO Dependencies Non Trivial FD ?
1 A→B  ×
2 A→C  ×
3 A→BC  ×
4 B→A  ×
5 B→C  ×
6 B→AC  ×
7 C→A  √
8 C→B  ×
9 C→AB  ×
10 AB→C  √
11 BC→A  √
12 AC→B  × 
A→B is not a non trivial FD because, for 2, it has two outputs. i.e 2→2 and 2→3.
for AB→C, 11→1, 12→1, 21→2, 22→3, so Non trivial.
Question 2:
 R(A B C D)
 AB {Candidate Key}
 A→C
 B→D .
 Where is the redundancy exist ?
Solution: (A C) and (B D) is suffering from redundancy.
Question 3:
Consider a relation with schema R(A,B,C,D) and FDs {AB -> C, C -> D, D -> A}. 
a. What are some of the nontrivial FDs that can be inferred from the given FDs?
Some examples:

C -> ACD
D -> AD
AB -> ABCD
AC -> ACD
BC -> ABCD
BD -> ABCD
CD -> ACD
ABC -> ABCD
ABD -> ABCD
BCD -> ABCD
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Types of FD
with Example – 		Inference Rules For
Functional Dependencies
     

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