SQL was explicitly designed to appeal to business people, and uses strictly familiar words and phrases. It was very explicitly designed (though I would say it has mostly failed) to read like pseudo-natural language.

SQL DBs and the precise semantics of SQL are somewhat based on relational algebra, but SQL syntax is definitely not. It's also not using set theoretic terms in general, with the exception of UNION and INTERSECT.

SQL tables are not actually sets at all since you can insert duplicate rows! In practice they usually are though.

You can't actually insert a complete duplicate row because the ROWID (or whatever your particular RDBMS calls it) is a implicit, but unique property of each row (and corresponds to the offset in the file the row is located at). Further, while tables can be the identity element of all records they contain, they themselves aren't really a set. Usually when people associate set theory with SQL, it's with queries (and their results).