GATE CS 2024 Set 1 — Question 35

To evaluate the expression $\sigma_{B<C}(R \bowtie_{R.A=S.A} S)$, we first perform the natural join (equi-join on attribute $A$) between relations $R$ and $S$, and then apply the selection condition $B < C$.Step 1: Perform the Join ($R \bowtie_{R.A=S.A} S$)
We match tuples from $R$ and $S$ where $R.A = S.A$.

• For $A=10$: $R$ has $(10, 20)$ and $S$ has $(10, 90)$.
• Resulting tuple: $(A=10, B=20, C=90)$
• For $A=20$: $R$ has $(20, 30)$ but $S$ has no tuple with $A=20$. No match.
• For $A=30$: $R$ has $(30, 40)$ and $(30, 50)$. $S$ has $(30, 45)$.
• Match $(30, 40)$ with $(30, 45) \rightarrow (A=30, B=40, C=45)$
• Match $(30, 50)$ with $(30, 45) \rightarrow (A=30, B=50, C=45)$
• For $A=40$: $S$ has $(40, 80)$ but $R$ has no tuple with $A=40$. No match.
• For $A=50$: $R$ has $(50, 95)$ but $S$ has no tuple with $A=50$. No match.

The intermediate relation after the join contains 3 tuples:Step 2: Apply Selection ($\sigma_{B<C}$)
We filter the joined tuples where the value of attribute $B$ is strictly less than attribute $C$.Step 3: Count the Tuples
The tuples satisfying the condition are $(10, 20, 90)$ and $(30, 40, 45)$.Total number of tuples = 2.