The relational model of data with two types of null values is considered. The basis for defining operations in such a model is three-valued logic; thus, three-valued relations of equality of tuples, relation membership, relation inclusion and equality, are introduced. Extended operations of relational algebra  are defined (``true'' and ``maybe'' operations, applicable to date extended by null values). Properties of those operations, analogous to the properties of operations of the basic relational algebra, are proved. Since the ability to change the order in which specific operations are executed influences query optimization, extended operations are proved to have that property too.