1
GATE CSE 2015 Set 3
+1
-0.3
Consider the relation $$X\left( {P,Q,R,S,T,U} \right)$$ with the following set of functional dependencies
\eqalign{ & F = \left\{ \, \right. \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left\{ {P,R} \right\} \to \left\{ {S,T} \right\}, \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left\{ {P,S,U} \right\} \to \left\{ {Q,R} \right\} \cr & \,\,\,\,\,\,\,\,\,\,\left. \, \right\} \cr}
Which of the following is the trivial functional dependency in $${F^ + },$$ where $${F^ + }$$ is closure of $$f$$ ?
A
$$\left\{ {P,R} \right\} \to \left\{ {S,T} \right\}$$
B
$$\left\{ {P,R} \right\} \to \left\{ {R,T} \right\}$$
C
$$\left\{ {P,S} \right\} \to \left\{ S \right\}$$
D
$$\left\{ {P,S,U} \right\} \to \left\{ Q \right\}$$
2
GATE CSE 2014 Set 1
+1
-0.3
Consider the relation schema $$R = \left( {E,\,F,\,G,\,H,\,I,\,J,\,K,L,\,M,\,N} \right)$$ and the set of functional dependencies $$\left\{ {\left\{ {E,F} \right\} \to \left\{ G \right\},\left\{ F \right\}} \right.$$
$$\to \left\{ {I,J} \right\},\left\{ {E,H} \right\} \to \left\{ {K,L} \right\},\left\{ K \right\}$$
$$\to \left\{ M \right\},\left\{ L \right\}$$
$$\to \left. {\left\{ N \right\}} \right\}$$ on $$R.$$ What is the key for $$R?$$
A
$$\left\{ {E,F} \right\}$$
B
$$\left\{ {E,F,H} \right\}$$
C
$$\left\{ {E,\,F,\,H,\,K,\,L} \right\}$$
D
$$\left\{ E \right\}$$
3
GATE CSE 2014 Set 3
+1
-0.3
A prime attribute of a relation scheme $$R$$ is an attribute that appears
A
In all candidate keys of $$R$$
B
In some candidate key of $$R.$$
C
In a foreign key of $$R.$$
D
Only in the primary key of $$R.$$
4
GATE CSE 2014 Set 2
Numerical
+1
-0
The maximum number of superkeys for the relation schema $$R(E, F, G, H)$$ with $$E$$ as key is ______.