GATE Papers >> CSE >> 2019 >> Question No 65

Question No. 65 CSE | GATE 2019

Consider the following relations P(X,Y,Z), Q(X,Y,T) and R(Y,V).

P
X Y Z
X1 Y1 Z1
X1 Y1 Z2
X2 Y2 Z2
X2 Y4 Z4

 

Q
X Y T
X2 Y1 2
X1 Y2 5
X1 Y1 6
X3 Y3 1

 

 

R
Y V
Y1 V1
Y3 V2
Y2 V3
Y2 V2

 

How many tuples will be returned by the following relational algebra query?

$ \prod\nolimits_X(\sigma_{\left(P.Y=R.Y\wedge R.V=V2\right)}(P\times R))-\prod\nolimits_X(\sigma_{\left(Q.Y=R.Y\wedge Q.T>2\right)}(Q\times R)) $


Answer : 1 to 1


Solution of Question No 65 of GATE 2019 CSE Paper

$ {\mathrm\pi}_{\mathrm x}\left({\mathrm\sigma}_{\left(\mathrm P.\mathrm Y=\mathrm R.\mathrm Y\wedge\mathrm R.\mathrm V=\mathrm V2\right)}\right)^{\left(\mathrm P\times\mathrm R\right)}) $

It joins P and R with condition of $ \left(\mathrm P.\mathrm Y=\mathrm R.\mathrm Y\wedge\mathrm R.\mathrm V=\mathrm V2\right) $ and it returns only one column that is X. The output will be one x'2

$ {\mathrm\pi}_{\mathrm x}\left({\mathrm\sigma}_{\left(\mathrm Q.\mathrm Y=\mathrm R.\mathrm Y\wedge\mathrm Q.\mathrm T>2\right)}\right)^{\left(\mathrm Q\times\mathrm R\right)}) $

It joins P and R with condition of $ \left(\mathrm Q.\mathrm Y=\mathrm R.\mathrm Y\wedge\mathrm Q.\mathrm T=\mathrm T>2\right) $ and it returns only one column that is X. The output will be two x'1 's but relational algebra eliminates duplication so here only x1.

$ {\mathrm\pi}_{\mathrm x}\left({\mathrm\sigma}_{\left(\mathrm P.\mathrm Y=\mathrm R.\mathrm Y\wedge\mathrm R.\mathrm V=\mathrm V2\right)}\right)^{\left(\mathrm P\times\mathrm R\right)})-{\mathrm\pi}_{\mathrm x}\left({\mathrm\sigma}_{\left(\mathrm Q.\mathrm Y=\mathrm R.\mathrm Y\wedge\mathrm Q.\mathrm T>2\right)}\right)^{\left(\mathrm Q\times\mathrm R\right)}) $ output will be only x2 so1 tuple has returned.

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