1
GATE CSE 2014 Set 3
+1
-0.3
What is the optimized version of the relation algebra expression $$\pi_{A1}(\pi_{A2}(\sigma_{F1}(\sigma_{F2}(r))))$$, where $$A1, A2$$ are sets of attributes in r with $$A1 \subset A2$$ and $$F1,F2$$ are Boolean expressions based on the attributes in r?
A
$$\pi_{A1}(\sigma_{(F1 \wedge F2)}(r))$$
B
$$\pi_{A1}(\sigma_{(F1 \vee F2)}(r))$$
C
$$\pi_{A2}(\sigma_{(F1 \wedge F2)}(r))$$
D
$$\pi_{A2}(\sigma_{(F1 \vee F2)}(r))$$
2
GATE CSE 2014 Set 3
+2
-0.6
Consider the relational schema given below, where eId of the relation dependent is a foreign key referring to empId of the relation employee. Assume that every employee has at least one associated dependent in the dependent relation:

employee (empId, empName, empAge)

dependent (depId, eId, depName, depAge)

Consider the following relational algebra query: $$\Pi_{empId}\:(employee) - \Pi_{empId}\:(employee \bowtie_{(empId=eID) \wedge (empAge \leq depAge)} dependent)$$

The above query evaluates to the set of empIds of employees whose age is greater than that of

A
some dependent.
B
all dependents.
C
some of his/her dependents.
D
all of his/her dependents.
3
GATE CSE 2014 Set 3
+2
-0.6
Consider the transactions T1, T2, and T3 and the schedules S1 and S2 given below.

T1 : r1 (X) ; r1 (Z) ; w1 (X) ; w1 (Z)

T2 : r2 (X) ; r2 (Z) ; w2 (Z)

T3 : r3 (X) ; r3 (X) ; w3 (Y)

S1: r1(X); r3(Y); r3(X); r2(Y); r2(Z); w3(Y); w2(Z); r1(Z); w1(X); w1(Z)

S2: r1(X); r3(Y); r2(Y); r3(X); r1(Z); r2(Z); w3(Y); w1(X); w2(Z); w1(Z)

Which one of the following statements about the schedules is TRUE?
A
Only S1 is conflict-serializable.
B
Only S2 is conflict-serializable.
C
Both S1 and S2 are conflict-serializable.
D
Neither S1 nor S2 is conflict-serializable.
4
GATE CSE 2014 Set 3
+1
-0.3
Consider the following combinational function block involving four Boolean variables $$x, y, a,$$
$$b$$ where $$x, a, b$$ are inputs and $$y$$ is the output.
Which one of the following digital logic blocks is the most suitable for implementing this function?
A
B
Priority encoder
C
Multiplexer
D
Flip-flop
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