Problem $2$: Given relation $T(A,B,C,D)$ with $F{D}^{\text{'}}$sAB$C$ and $CD.$

a$.$ Complete the closures for all subsets of R using the FDs provided.

b$.$ Determine all non$-$trivial FDs associated with our relation $R$ and the given FDs$.$

c$.$ Identify the key and all superkeys for relation R$.$

Keys:

Superkeys:

d$.$ Is the set of FDs given minimal? If not, find the minimal basis?