  In this paper, we investigate the relationship between the Hilbert functions
and the associated properties of the graded modules. To attain this, we
construct the graded modules from the sets of points in projective space,
$\mathbb{P}_k^n$ . We use a computer software package for algebraic
computations Macaulay2 to study the Hilbert functions and the associated
properties of the graded modules. Thereafter, we provide theoretical proofs of
the results obtained from Macaulay2 and finally, we give illustrative examples
to justify some of our results.
