Ace Page# 09, Q# 04

Question

What does the double arrow in options 2 & 4 mean ?

Comments

Double arrow is for multi-valued dependency.

Answer 1

B,C ->A not hold since

2,3 ->1 and

2,3 ->4 is present.

Comments

B -> C also does not hold over S then why not answer is option a.

3 -> {3,4}

Answer 2

Your  doubt: What is double arrow??

Double arrow denotes multivalued dependency

• multivalued dependency is a full constraint between two sets of attributes in a relation.
• In contrast to the functional independency, the multivalued dependency requires that certain tuples be present in a relation. Therefore, a multivalued dependency is also referred as a tuple-generating dependency.
• The multivalued dependency also plays a role in 4NF normalization

Eg: (course, book, lecturer)  

Because the lecturers attached to the course and the books attached to the course are independent of each other, this database design has a multivalued dependency; if we were to add a new book to the AHA course, we would have to add one record for each of the lecturers on that course, and vice versa.

course -> -> book and cousre->->lecturer

Solution

All options except 3 are correct

BC-> A says wehnever for each BC pair A should give same value

But we can see (1,2,3) and (4,2,3)

For same BC (2,3) we have different values for A. 1 and 4

Thus it doesnt hold  BC -> A

3is the answer

Comments

check ur solution again , i think BC->A is not hold but BC->> A is hold

http://infolab.stanford.edu/~ullman/fcdb/aut07/slides/mvds.pdf

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Sorry sir,

Typing mistake...

BC -> A is wrong

thanks for poiniting

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$B\rightarrow C$ is also not holding in relation $S$, for value $3$ it has 2 different value $3,4.$

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@hira so options 1 and 3 both should be correct solution, right?

Answer 3

Both option 1 and 3 seems to be incorrect dependencies, so they are the answers because in option 2 and 4, its mention that they both do follow multi value dependency but in 1 and 3 they haven’t

Answer 4

Option 1) B→ C will not holds for relation S, because for the same value of 3 we have 2 different values i.e 3 and 4. so if we given 3 we cant determine the value of C.

Option 2)  B-» C will holds ,the same explanation above(for the same value of 3 we have 2 different values i.e 3 and 4.)

Option 3) BC→ A   will not hold for relation S, because for the same value of 2,3 and 2.3 we have 2 different values i.e 1 and 4. so if we given 2.3 we cant determine the value of C.

Option 4)  BC-» A  will holds ,the same explanation above(for the same value of 3 we have 2 different values i.e 3 and 4.)

from the above instances, we can say that Option 1 and 3 will not hold.