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 . 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 :

Identify Non Trivial Functional Dependency ?
Solution :

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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