Question

Again, suppose we have a relation on attributes A, B, C, D, E, and F, and these functional dependencies hold: S = { B → DE, BF → C, CF → B, DF → AE }.

(a) Does it follow from S that B → A?

(b) Does it follow from S that CF → E?

(c) Does it follow from S that DF → B?

(d) Does it follow from S that BD → C?

(e) Does it follow from S that BF C → A?

Answer 1

set Given Funchonal Dependicies s=d. B-) DE BF-)C CFB DF-S A E B TO check if an ED A-JB can be derived from an FD set F (A)+ using ED Set F we have to find A B is of B is subset of (A) + then true. ca) B-) A BB3 & BDE Y A6 263+ does not follow from s so Bm) A CF JE 4CF3t = |CEBDE AY

from s' EE LCFY+ SO CF-DE follows (c) OF-B {OF 3t = 4 DFAEY B¢{DEBT follow from's SO. DF- B does not (a) BD-JC į BD3t = hBDESI CE & BD}+ SO. BD SC does not follow from 's e) BECJA LBFC HT = | BFC DE AY RAE & BF CB* so BFC A follows from's