  In this paper, we first determine the minimum possible size of an Fq-linear
set of rank k in PG(1, q^n). We obtain this result by relating it to the number
of directions determined by a linearized polynomial whose domain is restricted
to a subspace. We then use this result to find a lower bound on the number of
points in an Fq- linear set of rank k in PG(2, q^n). In the case k = n, this
confirms a conjecture by Sziklai in [9].
