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 ________

First, evaluate the natural join/equi-join $R \bowtie_{R.A=S.A} S$ on attribute $A$:

1. For $A = 10$:

   • $R$: $(10, 20)$

   • $S$: $(10, 90)$

   • Joined tuple: $(10, 20, 90)$

2. For $A = 20$: No matching tuple in $S$.

3. For $A = 30$:

   • $R$: $(30, 40)$ and $(30, 50)$

   • $S$: $(30, 45)$

   • Joined tuples: $(30, 40, 45)$ and $(30, 50, 45)$

4. For $A = 50$: No matching tuple in $S$.

Now, apply the selection condition $\sigma_{B < C}$ to the joined tuples:

• For $(10, 20, 90)$: $B = 20, C = 90 \implies 20 < 90$ is True.

• For $(30, 40, 45)$: $B = 40, C = 45 \implies 40 < 45$ is True.

• For $(30, 50, 45)$: $B = 50, C = 45 \implies 50 < 45$ is False.

Therefore, exactly 2 tuples satisfy the condition.