# Questions Based on Relational Algebra (Gate Questions Included)

## Questions Based on Relational Algebra (Gate Questions Included) -Part 2

```Question 21: Consider the relation Student(name,sex, marks) where the
primary key is shown underlined, pertaining to students
in a class that has at least one boy and one girl. What
does the following relational algebra expression
produce?

a) names of girl students with the highest marks
b) names of girl students with more marks than some boy student
c) names of girl students with marks less than some boy student
d) names of girl students with more marks than all the boy students
[GATE 2004]```
```Solution :

⇒ (d) is the right answer```
```Question 22 : Let R and S be two relations with the following schema
R(P,Q,R1,R2,R3)
S(P,Q,S1,S2)
Where {P,Q} is the key for both schemas.
Which of the following queries are equivalent?

a) Only I and II
b) Only I and III
c) Only I II and III
d) Only I III and IV
[GATE 2008]```
`Solution : Let the relation R(P,Q,R1,R2,R3) and S(P,Q,S1,S2) be`
 P Q R1 R2 R3 p1 q2 – – – p2 q2 – – – p3 q1 – – –
 P Q S1 S2 p1 q2 – – p2 q3 – –
```Case I ) The query join the relation R and S then project the column P
only.

Case II) The query project the column P from R and S and join these
projected column .

Case III) The given query project separately the column P and Q in both
relation R and S. The intersection produces only those column
which are common in both and finally projection produces the
result the column P.

Case IV) The given query project the column P and Q in both relations
R and S separately. The difference of say A and B produces those
only those column which are not in B but in A. And finally
projection produces the result the column P.

```
```Question 23: Given two relations R1 and R2, where R1 contains N1
tuples and R2 contains N2 tuples, and N2 > N1 > 0,
give the maximum and minimum possible sizes (in tuples)
for the result relation produced by each of the
following relational algebra expressions. In each case,
state any assumptions about the schemas for R1 and R2
that are needed to make the expression meaningful.
(a) R1 ∪ R2
(b) R1 ∩ R2
(c) R1 - R2
(d) R1 × R2
(e) σa=5(R1)
(f) πa (R1)
(g) R1/R2```
```Solution :
a) R1 ∪ R2
Assumption: R1 and R2 are union compatible
Min: N2
Max: N1 + N2
(b) R1 ∩ R2
Assumption: R1 and R2 are union compatible
Min: 0
Max: N1
(c) R1 - R2
Assumption: R1 and R2 are union compatible
Min: 0
Max: N1
(d) R1 × R2
Min: N1 * N2
Max: N1 * N2
(e) σa=5(R1)
Assumption: R1 has an attribute named a
Min: 0
Max: N1
(f) πa (R1)
Assumption: R1 has an attribute named a
Min: 1
Max: N1
(g) R1/R2
Assumption: The set of attributes of R2 is a subset of
the attributes of R1.
Min: 0
Max: 0```

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