Solution

correct option is 1)

ρ (Tempred, π_sid ((δ_color = _red Boats) ⋈ Reserves)), ρ (Tempgreen, π_sid ((δ_color = _green Boats) ⋈ Reserves)), π_sname (Tempred ∩ Tempgreen) ⋈ Sailors

It can be broken down as follows:

• π sid ((δ_color = _red Boats) ⋈ Reserves)) - This query selects the sailor IDs for all sailors who have reserved a red boat by selecting the reservation records for red boats and projecting only the sailor ID from the result. The result of this query is renamed to Tempred.
• π sid ((δ_color = _green Boats) ⋈ Reserves)) - This query does the same as the previous query, but for green boats instead of red boats. The result of this query is renamed to Tempgreen.
• Tempred ∩ Tempgreen - The intersection operator ∩ is used to find the sailor IDs that appear in both Tempred and Tempgreen, i.e., the sailor IDs of sailors who have reserved both red and green boats.
• π sname (Tempred ∩ Tempgreen) ⋈ Sailors - Finally, the result of the intersection is joined with the Sailors relation using the join operator ⋈, and the sailor name is projected from the result to give us the names of sailors who have reserved both red and green boats.

This query computes the names of sailors who have reserved both red and green boats. It does so by selecting the sailor IDs for sailors who have reserved red and green boats, intersecting the results to find the sailor IDs of sailors who have reserved both, and then joining this result with the Sailors relation to obtain the sailor names.