1
GATE CSE 2012
+2
-0.6
Suppose R1 (A, B) and R2 (C, D) are two relation schemas. Let r1 and r2 be the corresponding relation instances. B is a foreign key that refers to C in R2. If data in r1 and r2 satisfy referential integrity constraints, which of the following is ALWAYS TRUE?
A
$$\prod_{B}(r_{1})- \prod _{C}(r_{2})= \varnothing$$
B
$$\prod_{C}(r_{2})- \prod _{B}(r_{1})= \varnothing$$
C
$$\prod_{B}(r_{1}) = \prod _{C}(r_{2})$$
D
$$\prod_{B}(r_{1}) - \prod _{C}(r_{2}) \neq \varnothing$$
2
GATE CSE 2012
+2
-0.6
Consider the following transactions with data items P and Q initialized to zero:
T1 : read (P) ;
if P = 0 then Q : = Q + 1 ;
write (Q). 
T2 : read (Q) ;
if Q = 0 then P : = P + 1 ;
write (P).
Any non-serial interleaving of T1 and T2 for concurrent execution leads to
A
a serializable schedule
B
a schedule that is not conflict serializable
C
a conflict serializable schedule
D
a schedule for which precedence graph cannot be drawn
3
GATE CSE 2012
+2
-0.6
What is the minimal form of the Karnaugh map shown below? Assume that $$X$$ denotes a don’t care term.
A
$$\overline {bd}$$
B
$$\overline {bd} + \overline {bc}$$
C
$$\overline {bd} + a\overline {bc} d$$
D
$$\overline {bd} + \overline {bc} + \overline {cd}$$
4
GATE CSE 2012
+1
-0.3
Consider the following logical inferences.
$${{\rm I}_1}:$$ If it rains then the cricket match will not be played. The cricket match was played.
Inference: there was no rain.

$${{\rm I}_2}:$$ If it rains then the cricket match will not be played. It did not rain
Inference:the cricket match was played. which of the following is TRUE?

A
Both $${{\rm I}_1}$$ and $${{\rm I}_2}$$ are correct inferences
B
$${{\rm I}_1}$$ is correct but $${{\rm I}_2}:$$ is not a correct inference
C
$${{\rm I}_1}$$ is not correct but $${{\rm I}_2}$$ is a correct inference
D
Both $${{\rm I}_1}$$ and $${{\rm I}_2}$$ are not correct inferences
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