GATE CSE 1998 | Question: 1.33

Question

Given two union compatible relations $R_1(A, B)$ and $R_2 (C, D)$, what is the result of the operation $R_1 \Join_{ A = C \wedge B = D} R_2$?

• A. $R_1 \cup R_2$

• B. $R_1 \times R_2$

• C. $R_1 – R_2$

• D. $R_1 \cap R_2$

Comments

Detailed Video Solution: https://youtu.be/H4-GIPOm2DE?feature=shared

NOTE that the given "join" operation is Equi-Join, & hence the Schema of the result will be $(A,B,C,D)$, So, technically, no option is correct.

BUT Authors like Raghu Ramakrishnan project only one attribute from the equated attributes in Equijoin.

The schema of given Equijoin operation, as per Navathe & Ullman, will be $(A,B,C,D).$

The schema of given Equijoin operation, as per Raghu Ramakrishnan, will be $(A,B).$

Neverthless, Option D is the best choice. Watch the Video Solution above.

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taking small examples can help :
A  B           C   D
1  2            5   9
2  3            2   3
4  3            3   1
5  1            8   4
given expr will return (2  3)

Answer 1

This question is an example of Theta Join,

$r \bowtie_\theta s= \sigma_\theta(r \times s)$

The join here will be selecting only those tuples where $A = C$ and $B = D,$ meaning it is the intersection. D option.

Comments

.

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Right ABCD will be the final schema here

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The question can be equally transformed to : r1(ab) natural join r2(ab) with renaming cd

Answer 2

✍️ Example:

Let’s say:

R₁(A, B):

A	B
1	2
3	4
5	6

R₂(C, D):

C	D
3	4
5	6
7	8

🔗 Operation: R₁ ⋈A₌C ∧ B₌D R₂

We match rows where:

• A = C

• B = D

So we look for tuples that are identical in both tables.

✅ Matching tuples:

• ⟨3, 4⟩

• ⟨5, 6⟩

🎯 Result:

A	B	C	D
3	4	3	4
5	6	5	6

This is just the intersection of R₁ and R₂.