The design of SQL is based on a three-valued logic (3VL), rather than the familiar Boolean logic. 3VL adds a truth value unknown to true and false to handle nulls. Viewed as indispensable for SQL expressiveness, it is at the same time much criticized for unintuitive behavior of queries and being a source of programmer mistakes. We show that, contrary to the widely held view, SQL could have been designed based on the standard Boolean logic, without any loss of expressiveness and without giving up nulls. The approach itself follows SQL's evaluation, which only retains tuples for which conditions in WHERE evaluate to true. We show that conflating unknown with false leads to an equally expressive version of SQL that does not use the third truth value. Queries written under the two-valued semantics can be efficiently translated into the standard SQL and thus executed on any existing RDBMS. These results cover the core of the SQL 1999 Standard: SELECT-FROM-WHERE-GROUP BY-HAVING queries extended with subqueries and IN/EXISTS/ANY/ALL conditions, and recursive queries. We also investigate new optimization rules enabled by the two-valued SQL, and show that for many queries, including most of those found in benchmarks such as TPC-H and TPC-DS, there is no difference between three- and two-valued versions.