Given the Relational Model Notation below, extend it to define

Question

UNIQUE and NON-UNIQUE indexes for relations.

The uppercase letters Q, R, S denote relation names.
■ The lowercase letters q, r, s denote relation states.
■ The letters t, u, v denote tuples.
■ In general, the name of a relation schema such as STUDENT also indicates
the current set of tuples in that relation—the current relation state—whereas
STUDENT(Name, Ssn, …) refers only to the relation schema.
■ An attribute A can be qualified with the relation name R to which it belongs by using the dot notation R.A—for example, STUDENT.Name or
STUDENT.Age. This is because the same name may be used for two attributes in different relations. However, all attribute names in a particular
relation must be distinct.
■ An n-tuple t in a relation r(R) is denoted by t = <v1, v2, … , vn>, where vi is the value corresponding to attribute Ai. The following notation refers to
component values of tuples: Both t[Ai] and t.Ai (and sometimes t[i]) refer to the value vi in t for attribute Ai. Both t[Au, Aw, … , Az] and t.(Au, Aw, … , Az), where Au, Aw, … , Az is a list of attributes from R, refer to the subtuple of values <vu, vw, … , vz> from t corresponding to the attributes specified in the list.
As an example, consider the tuple t = <’Barbara Benson’, ‘533-69-1238’,
‘[phone]’, ‘7384 Fontana Lane’, NULL, 19, 3.25> from the STUDENT relation in Figure 5.1; we have t[Name] = <‘Barbara Benson’>, and t[Ssn, Gpa, Age] = <‘533-69-1238’, 3.25, 19>.