GATE DS&AI 2024 | Question: 36

Question

​​​​​​Given the relational schema $R=(U, V, W, X, Y, Z)$ and the set of functional dependencies:

\[
\{U \rightarrow V, U \rightarrow W, W X \rightarrow Y, W X \rightarrow Z, V \rightarrow X\}
\]

Which of the following functional dependencies can be derived from the above set?

• A. $V W \rightarrow Y Z$
• B. $W X \rightarrow Y Z$
• C. $V W \rightarrow U$
• D. $V W \rightarrow Y$

Answer 1

Given a set of functional dependencies derived from an attribute iff with the help of its closure, we can determine it.

$(VW)^+=VWXYZ$ we can determine $V,W,X,Y,Z$

$(WX)^+=WXYZ$ we can determine $Y,Z$

but
$(VW)^+$ can not determine $U$

Option $(A,B,D) $ true.