Functional Dependency Reduction

Question

I'm supposed to find the minimal cover for this set of FD's. 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)

Answer 1

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.