GATE CS 1998 Q1.33 — Relational Model: Relational Algebra

To find the result of the operation $R_1 \Join_{A = C \wedge B = D} R_2$, let us analyze the given conditions:

1. Union Compatibility: Since $R_1(A, B)$ and $R_2(C, D)$ are union-compatible, they have the same number of attributes, and the corresponding domains are compatible (i.e., $\text{dom}(A) = \text{dom}(C)$ and $\text{dom}(B) = \text{dom}(D)$).
2. Join Condition: The join condition is $A = C \wedge B = D$. This means we are looking for pairs of tuples $(a, b) \in R_1$ and $(c, d) \in R_2$ such that:
   • $a = c$
   • $b = d$

This condition matches only those tuples that are identical in both relations (i.e., present in both $R_1$ and $R_2$).

Conceptually, finding the set of tuples that exist in both $R_1$ and $R_2$ is equivalent to the set intersection operation:

Thus, the operation represents the intersection of the two relations.

Correct Option: D