Aug2016 cs Q9

0. Suppose database table T₁(P, R) currently has tuples {(10, 5), (15, 8), (25, 6)} and table T₂ (A, C) currently has {(10, 6), (25, 3), (10, 5)}. Consider the following three relational algebra queries RA₁, RA₂ and RA₃:
RA₁ : T₁ ⨝ _{T1.P = T2.A} T₂ where ⨝is natural join symbol
RA₂ : T₁ ⟕ _{T1.P = T2.A} T₂ where ⟕ is left outer join symbol
RA₃ : T₁ ⨝ _{T1.P = T2.A and T1.R = T2.C}T₂
The number of tuples in the resulting table of RA₁, RA₂ and RA₃ are given by:

Answer
Comment
Array

Option : D
Explanation :
RA₁ : T₁ ⨝ _{T1.P = T2.A} T₂ where ⨝is natural join symbol. It will result 3 tuples:
P = A R C
10 5 6
10 5 5
25 6 3
RA₂ : T₁ ⟕ _{T1.P = T2.A} T₂ where ⟕ is left outer join symbol. It will result in 4 tuples.
P = A R C
10 5 6
10 5 5
15 8 Null
25 6 3
RA₃ : T₁ ⨝ _{T1.P = T2.A} and T₁.R = T₂.C^T₂. It will result in 1 tuple.
P = A R = C
10 5
So, option (D) is correct.

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