GATE | GATE CS 2019 | Question 63

Consider the following relation P(X, Y, Z), Q(X, Y, T) and R(Y, V):




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

πx(σ(P.Y = R.Y ∧ R.V = V(P X R))) - πx(σ(Q.Y = R.Y ∧ Q.T > 2(Q X R))) 

Note: This was Numerical Type question.
(A) 3
(B) 1
(C) 2
(D) 4


Answer: (B)

Explanation: Query-1:

πx(σ(P.Y = R.Y ∧ R.V = V(P X R))) 

It will satisfy only one row:

X  Y  Z  Y  V
-------------------
X2  Y2  Z2  Y2  V2 
------------------- 

Only column X will be selected.

X 
-----
X2  
----- 

Query-2:

πx(σ(Q.Y = R.Y ∧ Q.T > 2(Q X R))) 

It will satisfy only two row:

X  Y  T  Y  V
-------------------
X1  Y2  5  Y2  V3
X1  Y1  6  Y1  V1 
------------------- 

Only column X will be selected.

X 
-----
X1 
----- 

Note that relational algebra return unique tuples only.

Now,

= πx(σ(P.Y = R.Y ∧ R.V = V(P X R))) 
= (Query-1) - (Query-2)
= X2 - X1
= X2 

So, answer is 1.

Note that {(Query-1) – (Query-2)} will return all tuples from query-1 those are not in query-2.


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