Question

Let R(A,B,C,D,E) be a relation with FDs F = {AB-C, CD-E, E-B, CE-A} Consider an instance of this relation that only contains the tuple (1, 1, 2, 2, 3). Which of the following tuples can be inserted into this relation without violating the FD's? (2 points) Select one: O (0, 1, 2, 4,3) (1,1,2,2,4) (1.2.2, 2, 3) o (1,1,3,2,3) All of the above can be inserted. None of the above can be inserted.

Answer 1

The Answer is None of the above can be inserted.

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When there is a functional dependency X->Y

the set of attributes in X should uniquely determine set of attributes in Y.

It means that each combination of values in X should precisely be related with one combination of Y.

Given relation: R(A, B, C, D, E)

F = {AB-->C, CD-->E, E-->B, CE-->A}

Tuple (1, 1, 2, 2, 3) already exists in R

Let us try inserting new tuple

>>>(0, 1, 2, 4, 3)

CE-->A is violated

Because C = 2, E = 3, A = 1 in existing tuple (1, 1, 2, 2, 3)

but C = 2, E = 3, A = 0 in newly inserted tuple  (0, 1, 2, 4, 3)

Same combination of C,E is related to two different values of A. Hence, CE-->A is violated

So this tuple cannot be inserted,

>>>(1, 1, 2, 2, 4)

CD-->E is violated

Because C = 2, D  = 2, E = 3 in existing tuple (1, 1, 2, 2, 3)

but C = 2, D = 2, E = 4 in newly inserted tuple  (1, 1, 2, 2, 4)

Same combination of C,D is related to two different values of E. Hence, CD-->E is violated

So this tuple cannot be inserted,

>>>(1, 2, 2, 2, 3)

E-->B is violated

Because E = 3, B =1 in existing tuple (1, 1, 2, 2, 3)

but E = 3, B = 2 in newly inserted tuple  (1, 2, 2, 2, 3)

Same combination of E is related to two different values of B .Hence, E-->B is violated

So this tuple cannot be inserted,

>>>(1, 1, 3, 2, 3)

AB-->C is violated

Because A = 1, B =1, C = 2 in existing tuple (1, 1, 2, 2, 3)

but A = 1, B =1, C = 3 i in newly inserted tuple  (1, 1, 3, 2, 3)

Same combination of A, B is related to two different values of C. Hence, AB-->C is violated

So this tuple cannot be inserted,

Hence

The Answer is None of the above can be inserted.

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