Question

3. What is the closure of {A, B} in R(A, B, C, D, E, F, G) with respect to the following sets of func- tional dependencies: (a) A+ ABD ABDEF + CG D+E ABC (b) D+A D+EF ABG C A+B AB +D

Answer 1

Solution:

Closure set of attribute is the set of attributes that can be derived from a given attribute set.

Question 1:

Closure set of {A,B} for R(A,B,C,D,E,F,G)

The functional dependencies are A->ABD,ABDEF->CG,D->E,AB->C

Here the closure of AB includes all attributes that can derive from AB.

SO {A,B}+={A,B,D,C,E} i.e

From First FD A-> ABD will include in closure of A

since attribute D is deriving from A D->E will also includes so {A,B,D,E}

similarly AB->C also included in the closure of A.where as second FD ABDEF->CG will not include because F is not derived by A.

so the final answer of {A,B}+ is {A,B,C,D,E}

Question 2:

The FD's are D->A,D->EF,ABG->CA->B,AB->D

So {A,B}+={A,B,D,E,F}

Here C and G is not included in closure of A since those attribues are not able to derive from A.

So for the second question {A,B}+ is {A,B,D,E,F}

Note: if you have any queries please post a comment thanks a lot....always available to help you..