Question

Let R(A,B,C,D) be a relation with FDs F = {A—B, AC, C-A, B,C, ABC-D} Which of the following statements is correct ? (2 points) Select one: G = {A-B, B-C, C-A, AC=D } is a canonical cover of F H = { AC, CA, BC,BD} is a canonical cover of F. o F is a canonical cover of itself. O G and H are canonical covers of F. None of the above.

Answer 1

Answer: None of the above.

• G can not be the canonical cover bacause in AC$\rightarrow$ D , C is extraneous. The reason is there is A $\rightarrow$ C in the set. So you can not keep C in AC $\rightarrow$ D.
• H is not a canonical cover because in the real set, Closure(A) has the attribute B. But in H, closure(A) does not have the attribute B i.e, Closure(A) in H ={A,C}. So this is not a canonical cover.
• F is not a canonical cover to itself because F can be reduced more. In ABC $\rightarrow$ D , B and C are extraneous. In A $\rightarrow$ B , B $\rightarrow$ C and C $\rightarrow$ A , C $\rightarrow$ A is trivial, so has to remove C$\rightarrow$A. So F is not a canonical cover.
• By the above we can say G and H are not canonical covers of F.
• So None of the above is the answer.