Compute Closure of AB and DC for given Relation and Fucntional Dependencies

Let

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

and

F = { AB → C, A → D, D → E, AC → B }

Then compute {AB}⁺ and {DC}⁺.

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

{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)

{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}

Asked in Year

2022

Course

BBM

University