An order is sometimes paid through several invoices, and sometimes paid without an invoice. In other words, there can be many Invoices per Order and many Orders per Invoice. This is a many-to-many relationship between Order and Invoice (also called a non-specific relationship). To represent this relationship in the database a new relvar should be introduced whose role is to specify the correspondence between Orders and Invoices: OrderInvoice (Order No, Invoice No) Now, the Order relvar has a one-to-many relationship to the OrderInvoice table, as does the Invoice relvar. If we want to retrieve every Invoice for a particular Order, we can query for all orders where Order No in the Order relation equals the Order No in OrderInvoice, and where Invoice No in OrderInvoice equals the Invoice No in Invoice. Set-theoretic formulation Basic notions in the relational model are relation names and attribute names. We will represent these as strings such as "Person" and "name" and we will usually use the variables and to range over them. Another basic notion is the set of atomic values that contains values such as numbers and strings. Our first definition concerns the notion of tuple, which formalizes the notion of row or record in a table: Tuple A tuple is a partial function from attribute names to atomic values. Header A header is a finite set of attribute names. Projection The projection of a tuple on a finite set of attributes is . The next definition defines relation that formalizes the contents of a table as it is defined in the relational model. Relation A relation is a tuple with , the header, and , the body, a set of tuples that all have the domain . Such a relation closely corresponds to what is usually called the extension of a predicate in first-order logic except that here we identify the places in the predicate with attribute names. Usually in the relational model a database schema is said to consist of a set of relation names, the headers that are associated with these names and the constraints that should hold for every instance of the database schema. Relation universe A relation universe over a header is a non-empty set of relations with header . Relation schema A relation schema consists of a header and a predicate that is defined for all relations with header . A relation satisfies a relation schema if