Given the following table T and the set of functional dependencies F:

T
A B C D
a1 b1 c1 d1
a1 b1 c2 d2
a2 b1 c1 d3
a2 b1 c3 d4
a2 b1 c4 d5

F = {A → B, C → B, D → ABC, AC → D}

a. What is the key for table T?
b. What is the highest normal form for table T? Please explain.

c. Given the following records or rows:
(a5, b6, c7, d8)
(a2, b2, c1, d8)
(a3, b1, c4, d3)
(a1, b1, c2, d5)

Please indicate which record can be added into table T without violating any of the functional dependencies in F. If the record or row cannot be legally added, please indicate which functional dependency is violated.