Functional Dependency Reduction

I'm supposed to find the minimal cover for this set of FD's. 开发者_运维问答Please let me know if my answer is correct.

1. XZ->Z
2. XZ->Y
3. XZ->B
4. YA->C
5. YA->G
6. C->W
7. B->G
8. XZ->G

My answer:

1. X->Z (deleted Z attribute, trivial FD)
2. Z->Y (deleted X, since it entails X->Z->Y from 1.)
3. Z->B (same here)
4. YA->C
5. YA->G
6. C->W
7. B->G
8. (Deleted, since X->Z->B->G)

It seem to me that the first one is not correct:

• XZ->Z does not imply anything, since XZ contains Z, thus it is trivial.

X->Z (deleted Z attribute, trivial FD)

The trivial part of XZ->Z is Z->Z. I don't think you can derive X->Z from XZ->Z.

If #1 is wrong, this #2 and #3 are also wrong.

Numbers 4-7 in your answer are right. (Your answer that's inside your question, that is.)

From your comment to Ziyao Wei,

1. XZ->Y 2. XZ->B 3. YA->C 4. A->G 5. C->W 6. B->G

Number 4 is wrong. Correct it, and you've found the minimal cover. Also, you said

I'm just confused about whether or not Y can be deleted from 4. if the implication is derived from XZ.

If you post your reasoning--how you derived A->G from XZ->Y and YA->C--then someone can probably show you where your reasoning went astray.