Question

In: Computer Science

Which of the following statements is true? Note that more than one of the statements may...

Which of the following statements is true? Note that more than one of the statements may be true.

a. Every relation that is in 3NF is in 2NF.

b. A relation that is in 2NF, and that has a non-primary-key attribute that is functionally dependent on another non-primary-key attribute is not in 3NF.

c. A relation that is in 2NF, and that has a non-primary-key attribute that is transitively functionally dependent on the primary key is not in 3NF.

Which of the following statements is true? Note that more than one of the statements may be true.

a. If A → B and C → D then B ∪ D is fully functionally dependant on A ∪ C, where X ∪ Y means the merge (or union) of X and Y.

b. If A → B and C→ D then A ∪ C→ B ∪ D, where X \cup∪ Y means the merge (or union) of X and Y.

c. If A is fully functionally dependant on B then B is fully functionally dependant on A.

d. If A → B then B → A.

Solutions

Expert Solution

a True

b false

c true

Explanation:

A relation schema R is in third normal form (3NF) if it is in 2NF and no non-prime attribute A in R is transitively dependent on the primary key.

a false

b True

Explanation

By rule in Composition:

If P holds Q (P → Q) and A holds B (A → B), then PA → QB.

C true

Explanation

The term full functional dependency (FFD) is used to indicate the minimum set of attributes in of a functional dependency (FD). In other words, the set of attributes X will be functionally dependent on the set of attributes Y if the following conditions are satisfied:

X is functionally dependent on Y and

X is not functionally dependent on any subset of Y.

In relation ASSIGN of table it is true that

FD: {EMP-ID,PROJECT, PROJECT-BUDGET} -> {YRS-SPENT-BY-EMP-ON PROJECT}

The values of EMP-ID, PROJECT and PROJECT-BUDGET determine a unique value of YRS-SPENT-BY-EMP-ON-PROJECT. However, it is not a full functional dependency because neither the EMP-ID -> YRS-SPENT-BY-EMP-ON-PROJECT nor the PROJECT -> YRS-SPENT-BY-EMP-ON-PROJECT holds true.

In fact, it is sufficient to know only the value of a subset of {EMP-ID, PROJECT, PROJECTBUDGET), namely, {EMP-ID, PROJECT}, to determine the YRS-SPENT-BY-EMP-ON PROJECT. Thus, the correct full functional dependency (FFD) can be written as:

FD: {EMP-ID,PROJECT} -> {YRS-SPENT-BY-EMP-ON-PROJECT}

d false

venereology answered 2 hours ago

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