Consider the relational schema of sailors $S$, Reserves $R$ and Boats $B$.Table 1: Sailors $S$

Sid	Sname	Rating	Age
22	Dustin	7	45.0
29	Brutus	1	33.0
31	Lubber	8	55.5
32	Andy	8	25.5
58	Rusty	10	35.5
64	Horatio	7	35.5
71	Zorba	10	16.0
74	Horatio	9	35.0
85	Art	3	25.5
95	Bob	3	63.5

Table 2: Reserves $R$

Sid	Bid	day
22	101	10/10/98
22	102	10/10/98
22	103	10/8/98
22	104	10/7/98
31	102	11/10/98
31	103	11/6/98
31	104	11/12/98
64	101	9/5/98
64	102	9/8/98
74	103	9/8/98

Table 3: Boats $B$

Bid	Bname	Color
101	Interlake	blue
102	Interlake	red
103	Clipper	green
104	Marine	red

Which of the following relational algebra query computes the Sid's of sailors with age over $20$ who have not reserved a red boat?

We need sailors whose age is over $20$ and who have not reserved a red boat.

First find sailors with age over $20$.

From Sailors table:

$\pi_{sid}(\sigma_{age>20}(Sailors))=\{22,29,31,32,58,64,74,85,95\}$

Now find red boats.

From Boats table, red boats are:

$Bid=102$ and $Bid=104$

Now find sailors who reserved red boats.

From Reserves table:

$Sid=22$ reserved $Bid=102$ and $Bid=104$

$Sid=31$ reserved $Bid=102$ and $Bid=104$

$Sid=64$ reserved $Bid=102$

So,

$\pi_{sid}((\sigma_{color='red'}(Boats))\bowtie Reserves\bowtie Sailors)=\{22,31,64\}$

Now subtract sailors who reserved red boats from sailors whose age is over $20$.

$\{22,29,31,32,58,64,74,85,95\}-\{22,31,64\}$

$=\{29,32,58,74,85,95\}$

So, the correct relational algebra expression must be:

$\pi_{sid}(\sigma_{age>20}(Sailors))-\pi_{sid}((\sigma_{color='red'}(Boats))\bowtie Reserves\bowtie Sailors)$