GATE CS 2024 Set 1 Q.35: Relational Algebra and Tuple Relational Calculus

Consider the following two relations, $R(A,B)$ and $S(A,C)$ :

The total number of tuples obtained by evaluating the following expression

\sigma_{B < C}(R \bowtie_{R.A = S.A} S)

is _________

Your answer

Official answer and solution

Solution

First compute the equijoin $R \bowtie_{R.A = S.A} S$ and then filter the resulting tuples using the condition $B < C$ .

Equijoin $R \bowtie_{R.A = S.A} S$ :
Matching tuples where $R.A = S.A$ $R . A = S . A$ (which occurs for $A = 10$ $A = 10$ and $A = 30$ $A = 30$ ) gives $3$ $3$ tuples:
- $(A = 10,\; B = 20,\; C = 90)$
- $(A = 30,\; B = 40,\; C = 45)$
- $(A = 30,\; B = 50,\; C = 45)$
Selection $\sigma_{B < C}$ :
- For $(10, 20, 90)$ : $20 < 90$ holds $\rightarrow$ selected.
- For $(30, 40, 45)$ : $40 < 45$ holds $\rightarrow$ selected.
- For $(30, 50, 45)$ : $50 < 45$ is false $\rightarrow$ discarded.

Thus, a total of 2 tuples are obtained.

Final answer

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