super key

Question

R ( A, B, C, D)

A & B are the candidate keys .

what are the possible  Super keys and there no ..??

Answer 1

Number of super keys with A =n(A)=A _ _ _ =2³

Number of Super keys with B =n(B)= _ B _ _ =2³

n(A∩B) = common super keys in A ,B = 4     (ABCD,ABC,ABD,AB)

Total Number of super keys with A,B are n(AUB)=n(A)+n(B)-n(A∩B) =8+8-4 = 12

those are A,AB,AC,AD ,B,BC,BD,ABD,ACD,ABC ,BCD,ABCD

Answer 2

A B

AB AC AD BC BD

ACD BCD ABC ABD

ABCD

THEY ARE 12

Answer 3

THIS IS WITH FORMULA POINT OF VIEW

A IS THE CANDIDATE KEY=>B,C,D ARE REST ATTRIBUTES=>NUM OF SUPER KEYS= 2^3=8

B IS THE CANDIDATE KEY=>A,C,D ARE REST ATTRIBUTES=>NUM OF SUPER KEYS= 2^3=8

C,D ARE THE COMMON ATTRIBUTES IN BOTH THE REST ATTRIBUTES => NUM OF KEYS=2^2=4

SO # OF SK=8+8-4=12

NOW WITH LOGIC

A IS CK=>{A,AB,AC,AD,ABC,ACA,ABD,ABCD}=8 NOS

B IS CK=>{B,BA,BC,BD,BAC,BAD,BCD,ABCD}=8 NOS

COMMON IN A AND B={AB,ABC,ABD,ABCD}=4 NOS

REMOVE COMMON=8+8-4=12