Consider a relation representing the present position of molecules in a closed container. The attributes are the ID for the molecule, the X, Y, and Z coordinates of the molecule, and its velocity in the X, Y, and Z dimensions. Refer to the X, Y, and Z coordinates as PX, PY, and PZ respectively, and the X, Y, and Z velocities as VX, VY, and VZ respectively.

a) What functional dependencies do you expect to hold?

b) What are the keys?

c) Other than the keys list three superkeys.

d) Other than the keys how superkeys are there?

Functional dependency can be defined as a constraint that is typically used to specify the relationship that exist between two (2) separate sets of attributes, in which one set can uniquely and accurately determine the actual value of the other attributes.

In this scenario, the coordinates of the molecule would be PX, PY, and PZ while the velocities of the corresponding coordinates are VX, VY, and VZ respectively. Thus, the functional dependencies include the following:

{PX, PY, PZ} ----> VX

{PX, PY, PZ} ----> VY

{PX, PY, PZ} ----> VZ

What are the keys?

The combination of keys in the R which can be used to get the molecule in the closed surface are as follows:

PX, PY, PZ

VX, VY, VZ.

What are the list of superkeys?

Superkeys refer to a set of attributes such as molecules, dimensions and velocities which can be used to hold a key. Thus, the list of superkeys are as follows:

PX, VX, VY, VZ.
PY, VX, VY, VZ.
PZ, VX, VY, VZ.

In conclusion, a superkey can be created when attribute are added to a primary key.

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