If the following functional dependencies holds on a selection R: A → B, A → C,…

To determine which functional dependency does not hold, we compute the closure of the left-hand side attributes for each option using the given functional dependencies (FDs): A → B, A → C, BC → D, C → F, B → E. Step 1: Compute closure of A (A+): A → B and A → C, so B and C are in A+. From B and C, BC → D, so D is in A+. From C, C → F, so F is in A+. From B, B → E, so E is in A+. Thus, A+ = {A, B, C, D, E, F}. Step 2: Compute closure of BC (BC+): BC → D, so D is in BC+. From C, C → F, so F is in BC+. From B, B → E, so E is in BC+. Thus, BC+ = {B, C, D, E, F}. Step 3: Compute closure of BD (BD+): B → E, so E is in BD+. D is in BD, but no FD has D as a left-hand side. C is not in BD+, and C → F, so F cannot be derived. Thus, BD+ = {B, D, E}, and F is not in the closure. Now evaluate each option: A → DE: A+ contains D and E, so this holds. BC → DEF: BC+ contains D, E, F, so this holds. A → EF: A+ contains E and F, so this holds. BD → EF: BD+ contains E but not F, so this does not hold.