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A relation R is in 2NF if every non-prime attribute of R is fully functionally dependent on every key of R  true or false

R(A,B,C)

F {A->B,B->C}

Here key = A

R is in 2NF

So is  C is fully functional dependent on every key here ?.

It is not dependent on key infact ?

2 Answers

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It is dependent on A due to transitivity property when A->B and B->C then A->C and the above relation is in 2NF.
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ANOTHER DEFINITON OF 2NF CAN BE:

A relation is in 2NF IF IT DOESNT HAVE PARTIAL FUCNTIONAL DEPENDENCIES(PD). PARTIAL FUNCTIONAL DEPENDENCIES ARE X->Y SUCH THAT X IS PART OF THE KEY AND Y IS NON PRIME ATTRIBUTE.

IN OTHER WORDS(PD MEANS PART OF THE KEY IS  DEPENDING ON THE NON PRIME ATTRIBUTE).

IF THERE IS A SINGLE KEY ATTRIBUTE THEN SUCH RELATION WILL ALWAYS BE IN 2NF(BECAUSE PART OF THE KEY CANT BE FORMED AND THERE WILL BE NO PD POSSIBLE )

SINCE IN YOUR QUESTION A IS  THE KEY SO PART OF IT IS NOT POSSIBLE ,SO NO PD ARE POSSIBLE AND THEREFORE RELATION IS IN 2NF.

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