Primary key attributes cannot have NULL values.

Alternate Key: A candidate key that is not chosen as the primary key.

Foreign Key: A set of attributes in a relation that refers to the primary key of another relation (or the same relation). It establishes a link between tables and enforces referential integrity.

The domain of the foreign key attributes must be compatible with the domain of the primary key attributes it references.
Foreign key values can be NULL if the foreign key is not part of the primary key of its own table, unless explicitly constrained otherwise.

Question: In a STUDENT table with attributes (StudentID, Name, Email, SSN), assume StudentID, Email, and SSN are all unique. Identify all candidate keys, the primary key (if StudentID is chosen), and any alternate keys.

3.4 Integrity Constraints

Rules that ensure the quality and consistency of data in a database.

Domain Constraints: Each attribute value must be from its specified domain.
Entity Integrity Constraint: The primary key of a relation cannot contain NULL values. This ensures that every tuple can be uniquely identified.
Referential Integrity Constraint: If a foreign key in relation $R_1$ refers to the primary key of relation $R_2$, then every value of the foreign key in $R_1$ must either be equal to a value of the primary key in $R_2$ or be NULL.
- Actions on Delete/Update of Referenced Primary Key:
  - Restrict: Prevent deletion/update if there are referencing foreign key values.
  - Cascade: Delete/update referencing foreign key values as well.
  - Set Null: Set referencing foreign key values to NULL.
  - Set Default: Set referencing foreign key values to a default value.
Check Constraints: User-defined conditions that a column's values must satisfy.
- Example: CHECK (Salary > 0)

Question: Explain why NULL values are generally not allowed in a primary key, relating your answer to the purpose of a primary key.

3.5 Relational Algebra

A procedural query language that takes relations as input and produces relations as output. It forms the theoretical basis for SQL.

Unary Operations (operate on a single relation):
- Selection ($\sigma$): Selects a subset of tuples from a relation that satisfy a selection condition $P$.
  - Notation: $\sigma_P(R)$
  - Example: Find all students majoring in 'CS'.
    $\sigma_{\text{Major = 'CS'}}(\text{STUDENT})$
- Projection ($\pi$): Selects a subset of attributes (columns) from a relation. Eliminates duplicate tuples by default.
  - Notation: $\pi_{A_1, A_2, ..., A_k}(R)$
  - Example: Get the names of all students.
    $\pi_{\text{Name}}(\text{STUDENT})$
- Rename ($\rho$): Renames a relation or its attributes.
  - Notation: $\rho_{S(B_1, ..., B_n)}(R)$ (renames relation $R$ to $S$ and its attributes to $B_1, ..., B_n$).
  - Notation: $\rho_S(R)$ (renames relation $R$ to $S$).
Binary Operations (operate on two relations):
- <