Relational algebra is a formal language for manipulating relational databases. It provides a set of mathematical operations that can be used to manipulate tables or relations, which are the fundamental data structure in a relational database. Relational algebra operations include selection, projection, union, intersection, difference, join, and division.

A tuple in a relational database is a row in a table or relation, which contains a set of related attributes or fields. Tuples are used to represent a single entity or record in the database. For example, in a table of employees, each tuple would represent a single employee, and each attribute in the tuple would represent a specific piece of information about that employee, such as their name, age, or job title.

Domain relational calculus is another formal language for manipulating relational databases. It is based on mathematical logic, and it provides a way to describe the desired results of a database query in terms of logical formulas or expressions. In domain relational calculus, the user specifies the desired results in terms of a set of conditions that the results must satisfy. The system then uses these conditions to generate the necessary code to retrieve the results. The main advantage of domain relational calculus is that it allows the user to express complex queries in a concise and precise way, using a well-defined mathematical language.