Function Dependency question

Question

Consider a relation R(A,B,C,D,E,F,H) with A as the only key. Assume that the dependencies E->F and C-> DEH hold.on R.

1. Is R in 2NF? If not, decompose to 2NF.

2. is R in 3NF? if not, decompose to 3NF.

//What does " with A as the only key" mean ?

Comments

"with A as the only key" I think it means A is the only key attribute and other (B,C,D,E,F,H) are non primary attribute so we can say that it is already in 2NF.

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But then, what is the relation between A and the remaining elements in R.

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As 'A' is the key attribute all other elements are depended on A. Like A->BCDEFH automatically holds.

Answer 1

R is in 2NF. It is NOT in 3NF. 3NF decomposition : ABC, CDEH, EF

A is the only candidate means that there are no other candidate keys.

Answer 2

R(ABCDEFH) { E → F, C → DEH}

here, Candidate key will be {ABC}.   So, C –> DEH is a partial functional dependency. So, its not in 2NF.

2NF decomposition will be: R1(CDEHF), R2(ABC)

 

Also, since its not in 2NF. so its also not in 3NF.

For 3NF decomposition will be: R1(EF), R2(CDEH), R3(ABC)