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We have a database table with relational schema R(XYZPQ): X Y Z P Q A1 B1 C1 D1 E1 A2 B2 C1 D2 E1 A3 B2 C2 D1 E2 A4 B3 C1 D3 E3 A5 B2 C2 D4 E2   Which of the following statements is true?

We have a database table with relational schema R(XYZPQ): X Y Z P Q A1 B1 C1 D1 E1 A2 B2 C1 D2 E1 A3 B2 C2 D1 E2 A4 B3 C1 D3 E3 A5 B2 C2 D4 E2   Which of the following statements is true? Correct Answer ZP → Q is a functional dependency.

The correct answer is option 1.

Concept:

Functional Dependency:

A functional dependency is a constraint that specifies the relationship between two sets of attributes where the one set can accurately determine the value of other sets.

It is denoted as X → Y, where X is a set of attributes that is capable of determining the value of Y. The attribute set on the left side of the arrow, X is called Determinant, while on the right side, Y is called the Dependent.

The given relational schema R(XYZPQ):

Index X    Y     Z      P       Q    
1 A1 B1 C1 D1 E1
2 A2 B2 C1 D2 E1
3 A3 B2 C2 D1 E2
4 A4 B3 C1 D3 E3
5 A5 B2 C2 D4 E2

Option 1: ZP → Q is a functional dependency.

True, ZP→ Q is a functional dependency Here ZP is a set of attributes that is capable of determining the value of Q. All are uniquely determinable.

C1 D1 E1
C1 D2 E1
C2 D1 E2
C1 D3 E3
C2 D4 E2

Option 2: YZ → P is a functional dependency.

False, YZ → P is not a functional dependency because YZ is a set of attributes that is not capable of determining the value of P.

B2 C2 D1
B2 C2 D4

Option 4:Y→ X is a functional dependency   

False, Y→ X is a not functional dependency. Here Y is a set of attributes that is not capable of determining the value of X.

B2 A2
B2 A3
B2 A5

Hence the correct answer is ZP → Q is a functional dependency.

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