GATE CS 2024 Set 1 Q25 — Relational Model: Relational Algebra

To find the total number of tuples in the expression $\sigma_{B < C}\left(R \bowtie_{R.A=S.A} S\right)$, we evaluate it in two steps:

Step 1: Perform the Join ($R \bowtie_{R.A=S.A} S$)

We match tuples from $R$ and $S$ where the attribute $A$ is equal:

• For $A = 10$:
  • $R$ has $(10, 20)$ and $S$ has $(10, 90) \implies$ $(10, 20, 90)$
• For $A = 30$:
  • $R$ has $(30, 40)$ and $S$ has $(30, 45) \implies$ $(30, 40, 45)$
  • $R$ has $(30, 50)$ and $S$ has $(30, 45) \implies$ $(30, 50, 45)$

No other values of $A$ (i.e., $20, 40, 50$) have matching tuples in both relations.

Step 2: Apply the Selection ($\sigma_{B < C}$)

Now, we filter the joined tuples using the condition $B < C$:

1. For $(10, 20, 90)$: $20 < 90$ is True (Selected)
2. For $(30, 40, 45)$: $40 < 45$ is True (Selected)
3. For $(30, 50, 45)$: $50 < 45$ is False (Not selected)

Thus, the final relation contains exactly 2 tuples.