Lecture 2

Question 1

What is π_{A1, A2, …, An}(R)?

Answer 1

This is the projection, that denotes a relation based on R, that only comprimises only attributes A1, A2, A3, …, An from R

E.g. π_title(Movies) would only return a tuple of movie titles

Question 2

What is σ_C(R)?

Answer 2

Returns a new relation on R which comprises only tuples from R that meet condition C

Question 3

What is a Cartesian product?

Answer 3

A x B = {(a, b) | a in A and b in B}

Question 4

What is the Natural Join?

Answer 4

You naturally combine the tuples that match along the attributes that are both in the schema of R and S

Question 5

What is a Theta-Join?

Answer 5

Join if a certain condition is equal

Question 6

What is the notation to rename?

Answer 6

ρ_{S(B1, B2, …, Bn​)} (R), this renames R to B

Question 7

What is a superkey?

Answer 7

Any set of values that is able to uniquely identify a row in a table.

Question 8

What is functional dependency?

Answer 8

If for any two tuples that agree on their components for {A1, …, An} they must also agreen in {B1, … Bn}

Question 9

How can A1 … An –> B1 … Bm be rewritten?

Answer 9

A1 … An –> Bi for i = 1, …, m

Question 10

What is a closure of a set?

Answer 10

It returns what is functionality determined determined by A under S?

Question 11

What is the algorithm of a closure?

Answer 11

1. If necessary split the FD’s of S, so each FD in S has a single attribute on the right
2. Let X be a set of attributes that eventually will become the closure. Initialize X to be {A1, A2, …, An}
3. Repeatedly search for some FD B1B2…Bm –> C
   st. all of B1, B2, …, Bm are in the set of attributes X but C is not. Add C to the set X and repeat the search. Since X can only grow, and the number of attributes of any relation schema must be finite, eventually nothing more can be added to X, and this step ends.
4. The set X, after no more attirbutes can be added to it, is the correct value of {A1, A2, …, An }+

Question 12

What are the requirements of the minimal basis?

Answer 12

A minimal basis B for S satisfies three conditions:

1. All FDs in B have sinngleton right hand sides
2. If any FD is removed from B, it is no longer a basis for S
3. if for any FD we remove one or more attributes from the left hand side it is no longer a basis for S

Question 13

What is the relation schema of a relation?

Answer 13

It denotes the name of the table and what is in it. E.g. Movie(name, length, studio, year)

Question 14

How to find a minimal basis?

Answer 14

1. Make sure every relation has just one element at the RHS
2. Ignore one FD, check if the closure of the LHS is still the same as before, if so, then it can be dropped.