A: Compute closure of AB ad DC

Given Relation:

R = {A, B, C, D, E}

Given Functional Dependencies:

AB C
A D
D E
AC B

 

Closure of AB

{AB}+ = {AB} (axiom of reflexivity)

      = {ABC} (by union rule & given FD: AB C)

      = {ABCD} (by union rule & given FD: A D)

      = {ABCDE} (by union rule & given FD: D E)


Closure of DC

{DC}+ = {DC} (axiom of reflexivity)

      = {DCE} (by union rule & given FD: D E)

 

Hence,


Closure of AB, {AB}+ = {ABCDE}

and

Closure of DC, {DC}+ = {CDE}