Test: Functional Dependency - Computer Science Engineering (CSE) MCQ

By applying these rules repeatedly, we can find all of F+, given F.

It is possible to use Armstrong’s axioms to prove that Pseudotransitivity rule is sound.

Lossy-join decomposition is the decomposition used here .

A superkey is a combination of columns that uniquely identifies any row within a relational database management system (RDBMS) table.

The SQL NATURAL JOIN is a type of EQUI JOIN and is structured in such a way that, columns with same name of associate tables will appear once only.

The closure of F, denoted as F⁺, is the set of all regular FD, that can be derived from.

For trivial functional dependency,

Let A and be two sets consists of attributes of a relation

A → B

A ⊇ B 

Option 1: 

{X, Z} → {Z, W}

{X, Z}  ⊉ {Z, W}

Not a trivial functional dependency

Option 2: 

{X, V} → {V}

{X, V} ⊇ {V}

It is a trivial functional dependency

Option 3: 

{X, W, V} → {Y}

{X, W, V} ⊉  {Y}

Not a trivial functional dependency

Option 4: 

{Y, W } → {Y, X}

{Y, W } ⊉ {Y, X}

Not a trivial functional dependency

The query can be satisfied by any of the two options.

The left side and the right side of a functional dependency are sometimes called "determinant" and "dependent", respectively.

In a functional dependency, the determinant is the set of one or more attributes that determine the values of another set of attributes, called the dependent attributes. The determinant is typically on the left-hand side of the functional dependency arrow (→), while the dependent attributes are on the right-hand side.

For example, if we have a functional dependency A→B, it means that the values of attribute B are determined by the values of attribute A. In this case, A is the determinant and B is the dependent attribute.

The other options listed are not typically used to describe the left and right sides of a functional dependency. Here is a brief explanation of each:

• Domain; Attributes - The domain refers to the set of all possible values that an attribute can take, while attributes are the specific properties of an entity or relation. These terms are not typically used to describe the left and right sides of a functional dependency.
• Tuple; Relation - A tuple is a single row or record in a relation, while a relation is a set of tuples that share the same attributes. These terms are not typically used to describe the left and right sides of a functional dependency.
• Range; Table - The range is the set of all possible output values of a function, while a table is a collection of related data stored in rows and columns. These terms are not typically used to describe the left and right sides of a functional dependency.

 
Therefore, the correct answer is "Determinant; Dependent".

Use the union rule to replace

EF → G and EF → H 

EF → GH

F = { A → B  ABCD → E  EF → GH  ACDF → EG }

B is extraneous in ABCD → E because B ∈ ABCD and {A → B, ABCD → E, EF → GH, ACDF → EG}

logically implies {A → B, ACD → E, EF → GH, ACDF → EG}.

This is because every  ACD → E.

This FD can be derived using Armstrong’s Axioms from A → B and ABCD → E via transitivity rule

So remove B from ABCD → E.

F = { A → B ACD → E  EF → GH ACDF → EG }

E is extraneous in ACDF → EG because E ∈ EG and {A → B, ACD → E, EF → GH, ACDF → G}

logically implies {A → B, ACD → E, EF → GH, ACDF → EG}

remove E from ACDF → EG

F = { A → B ACD → E EF → GH ACDF → G}

G is extraneous in ACDF → G. Note that ACDF → G is already implied by ACD → E and EF → GH in F

remove ACDF → G from F.

None of the remaining FD's in F have extraneous attributes so the minimal cover is

A → B, ACD → E, EF → G, EF → H.

Certainty Factor (CF) is a numeric value that tells us how likely an event or a statement is supposed to be true.

This value is similar to probability, but with only probability value of any event agent cannot decide what to do. This certainty factor is decided through which the agent can decide whether to declare the statement true or false based on the probability and other knowledge that the agent has.

Dynamic Certainty for a Conclusion :

CF(C) = CF(H) x CF(R) , C is the conclusion

CF(H) = calculated Certainty Factor for Hypothesis.

R = given rule , "if H then C with certainty CF(R)"

Conjunction and Disjunction of Hypotheses:

CF (P1 and P2) = MIN { CF(P1) , CF(P2) }
CF (P1 or P2) = MAX { CF(P1) , CF(P2) }

Here, P1 , P2 are premises.

Given Rule is (P1 and P2) or P3

R1 and R2 are conclusions of rules.

CF(R1)= 0.8 

CF(R2)=0.3

CF(P1)=0.5  , CF(P2)=0.8 , CF(P3)=0.2

Where P1,P2,P3 are premises.

Now the CF of given rule ((P1 and P2) or P3)=   MAX  { MIN{CF(P1),CF(P2)} , CF(P3) } 

= MAX { MIN { 0.5,0.8} ,0.2}

=MAX { 0.5 , 0.2 }

= 0.5

Now, CF of R1 based on premises = 0.5 × CF(R1) =0.5 × 0.8 =0.40

Now, CF of R2 based on premises = 0.5 ×  CF(R2) =0.5 × 0.3 =0.15