**Set Intersection Operation (⋂):**

- This operation returns a relation with tuples that exist in both input relations.
- Written as
`r ⋂ s = r - (r - s)`

, where`-`

represents set difference. - In simpler terms, it gives you common elements between two sets.

**Natural Join Operation (⨝):**

- Combines two relations based on matching attributes.
- Forms a cartesian product, applies a selection on common attributes, and removes duplicates.
- Denoted by the join symbol ⨝.
- In simpler terms, it’s like combining two sets where certain attributes are equal.

**Division Operation (÷):**

- Denoted by the symbol ÷.
- Given two relations,
`r ÷ s`

produces a relation on the schema R – S. - A tuple is in the result if it satisfies specific conditions related to projection and matching attributes.
- Essentially, it represents a kind of filtering or extracting operation based on certain conditions.

**Assignment Operation (←):**

- Denoted by the symbol ←.
- Similar to assignment in programming languages, it allows you to store the result of a relational algebra expression into a variable.
- Useful for simplifying complex expressions and improving readability.

These operations provide a way to manipulate and combine relations in a relational database, helping to express more complex queries and operations.