Let $V$ be a finite dimensional vector space over $\mathbb R$ and let $f$ and $g$ be
two non-zero linear functionals on V such that whenever $f(x) ≥ 0$, we also
have that $g(x) ≥ 0.$ Which of the following statements are true?
a. $ker(f) ⊂ ker(g).$
b. $ker(f) = ker(g).$
c.$ f = αg$ for some $α > 0.$