Consider a database consisting of the relations, where the primary key of each relation is bolded.
sailors (sid, sname, rating, age)
boats (bid, bname, color)
reserved (sid, bid, date)
Find all sailor id's of sailors who have a rating of at least 8 or reserved boat 103.
Answer given is:
$π_{\mbox{sid}}\left [σ_{\mbox{rating} \geq 8} (S) \right ] \cup π_{\mbox{sid}} \left [ σ_{\mbox{bid}=103} (R) \right ]$
Why can we use a union in the solution? The selection of all sailors with a rating of at least 8 would return rows with all 4 attributes but the projection of sailors who rented boat 103 would only return the sid, right? I thought the two sets had to have the same arity.
When you project you just get the sid's. So you are taking the union of two sets of sid's.