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Why all normalization rules are defined only for non trivial dependencies ?does trivial dependencies satisfies all normal forms ?if yes then why it satisfies all normal forms? please explain by giving suitable examples?

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Yes, trivial dependencies satisfies all normal forms.

Trivial FD: X-->Y  when Y proper subset of X

Now in a relation Xi --> Yi

if for any Y (i.e. dependent) is a proper subset of any X (i.e. determinant) then always every X will be the super key atleast if not Primary key

In other words we can say for any relation if we have all the FD's as trivial i.e. all the determinant will be Super key and hence in BCNF (in BCNF, the determinant of all the dependency should be SK) and theryby in 1Nf, 2Nf and 3NF also.

So we can say indirectly the normalisation (except 4NF and 5NF) rules are defined only for non trivial dependencies.

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