Given two tables 𝑅1(𝑥,𝑦) and 𝑅2(𝑦,𝑧) with 50 and 30 number of tuples…

Answer: 1500

Reasoning:

• For each value of y, let count_R1(y) be the number of tuples in the first table with that y, and count_R2(y) be the number in the second table with that y.

• The number of joined tuples contributed by a particular y value equals count_R1(y) × count_R2(y).

• The total size of the join is the sum over all y values: Σ_y count_R1(y) × count_R2(y).

• Given only the totals (Σ_y count_R1(y) = 50 and Σ_y count_R2(y) = 30), this sum of products is maximized when all tuples from both tables share the same y value, because concentrating counts on a single value maximizes the product.

• In that case the join size is 50 × 30 = 1500, which is the maximum possible.

Note: The minimum possible join size is 0 if there are no matching y values between the two tables.