Gate19

Question

Answer 1

1
{x1}-{x2}

Comments

Plz explain I'm a bit confused for it to be 0

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Part 1
required rows :
p.y=r.y and r.v=v2
so you get
x2 y2 v2

part 2
q.y=r.y and t>2
so you get
x1 y2 v3

these 2 sets don't have any common value of x
therefore you will get the cardinality of 1st

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This was for how many marks?

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2mrk

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Manisha...r u sure..I also got x1 - x2..

Answer 2

in my gate 2019 paper I have got table data bit different compared to this question. when I solved that question I have got answer as 1. for this particular question answer would be zero only. Please check below.

as operation ∧ is commutative, we better find out R.V=V2 first.σ(P.Y=R.Y ∧ R.V=V2)(P × R)

R.V=V2

Y	V
y3	v2
y2	v2

σ(P.Y=R.Y ∧ R.V=V2)(P × R)

 

X	Y	Z	V
x2	y2	z2	v2
x2	y2	z4	v2

∏x(σ(P.Y=R.Y ∧ R.V=V2)(P × R))

so when we project column x from the above relation we get  (i.e : as no relation should contain duplicate elements)

X

x2

similarly for σ(Q.Y=R.Y ∧ Q.T>2)(Q × R) we get it as below.

Q.T>2

X	Y	T
x1	y2	5
x2	y1	6

σ(Q.Y=R.Y ∧ Q.T>2)(Q × R)

X	Y	T	V
x1	y2	5	v3
x1	y2	5	v2
x2	y1	6	v1

when we project column x from the above relation we get 

X
x1
x2

(i.e : as no relation should contain duplicate elements)

∏x(σ(P.Y=R.Y ∧ R.V=V2)(P × R)) - ∏x(σ(Q.Y=R.Y ∧ Q.T>2)(Q × R))

the final result is {x2} - {x1, x2} it should be nothing

so answer should be 0 for this question.