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List all functional dependencies satisfied by the relation.

Mumbai University > Information Technology > Sem 3 > Database Management System

Marks: 5M

Year: May 2015

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The functional dependencies satisfied by the relation are as follows:

• A → B

For the tuples t1(A1,B1,C1) and t2(A1,B1,C2), t1 (A) =t2(A)=A1 and t1(B)=t2(B)=B1. Thus, the functional dependency A→B is satisfied by the relation.

• C → B

For the tuples t1(A1,B1,C1) and t3(A2,B1,C2), t1 (C) =t3(C) =C1 and t1 (B)=t3(B)=B1. Thus, the functional dependency C→B is satisfied by the relation.

• The dependency AC→B can also be obtained.

Following are the functional dependencies which are not satisfied.

• C does not functionally determine A because the tuples t1(A1,B1,C1) and t3(A2,B1,C1) have the same C but different A values.
• The same tuples also show B does not functionally determine A.
• A does not functionally determine C because the first two tuples t1(A1,B1,C1) and t2(A1,B1,C2)have the same A value and different C values.
• The same tuples also show B does not functionally determine C.