GATE Overflow Test Series | Mock GATE | Test 4 | Question: 24

Question

For the relation $R(A,B,C,D),$ on which the following functional dependencies hold $F:\{A \rightarrow B,B\rightarrow C, C \rightarrow A\}, G:\{A \rightarrow BC, B \rightarrow A, C \rightarrow A\}.$ Which of the following is correct?(Mark all the appropriate options)

• A. $F$ covers $G$
• B. $G$ covers $F$
• C. $F \equiv G$
• D. $F \not\equiv G$

Answer 1

Here, $F$ covers $G$, which means $F^{+} \supseteq G.$

And, $G$ covers $F$, which means $G^{+} \supseteq F.$
 
$\therefore F \equiv G.$
    
So, the correct answer is $A;B;C.$